Updated on 2026/04/03

写真a

 
OYA HIRONORI
 
Organization
School of Science Associate Professor
Title
Associate Professor
Homepage
https://hironorioya.github.io/
External link

Degree

  • Ph.D of Mathematical Sciences ( 2017.3   The University of Tokyo )

Research Interests

  • Quantum groups

  • Representation theory

  • Crystal bases

  • Canonical bases

  • Categorification

  • Cluster algebras

Research Areas

  • Natural Science / Algebra  / Representation theory

Education

  • The University of Tokyo   Graduate School of Mathematical Sciences   Ph.D course

    2014.4 - 2017.3

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  • The University of Tokyo   Graduate School of Mathematical Sciences   Master course

    2012.4 - 2014.3

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  • The University of Tokyo   School of Science   Department of Mathematical Sciences

    2008.4 - 2012.3

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Research History

  • Institute of Science Tokyo   Department of Mathematics   Associate Professor

    2024.10

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    Country：Japan

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  • Tokyo Institute of Technology   Department of Mathematics   Associate Professor

    2022.8 - 2024.9

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    Country：Japan

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  • Shibaura Institute of Technology   College of Systems Engineering and Science Department of Mathematical Sciences   Associate Professor

    2021.4 - 2022.7

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    Country：Japan

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  • Shibaura Institute of Technology   College of Systems Engineering and Science Department of Mathematical Sciences   Assistant Professor

    2018.9 - 2021.3

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    Country：Japan

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  • Université Paris Diderot   Institut de Mathématiques de Jussieu - Paris Rive Gauche   Post-doctoral researcher

    2017.9 - 2018.8

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    Country：France

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  • The University of Tokyo   Graduate School of Mathematical Sciences   Associate fellow

    2017.4 - 2017.8

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    Country：Japan

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  • The University of Tokyo   Graduate School of Mathematical Sciences   Japan Society for the Promotion of Science Research Fellowship for Young Scientists (DC2)

    2015.4 - 2017.3

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    Country：Japan

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  • The University of Tokyo   Graduate School of Mathematical Sciences   Frontiers of Mathematical Sciences and Physics Course student

    2012.11 - 2017.3

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    Country：Japan

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Professional Memberships

Committee Memberships

  • Sugaku   Editorial Board  

    2025.7 - 2027.6   

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    Committee type：Academic society

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  • Kodai Mathematical Journal   Editorial Board  

    2022.8   

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Papers

  • A note on a cluster structure of the coordinate ring of a simple algebraic group Reviewed

    Hironori Oya

    Proceedings of the American Mathematical Society   154 ( 5 )   1867 - 1879   2026.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    We show that the coordinate ring of a simply-connected simple algebraic group $G$ over the complex number field coincides with the Berenstein–Fomin–Zelevinsky cluster algebra and its upper cluster algebra, at least when $G$ is not of type $F_4$.

    DOI： 10.1090/proc/17551

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    Other Link： https://www.ams.org/proc/0000-000-00/S0002-9939-2026-17551-2/S0002-9939-2026-17551-2.pdf

  • Newton–Okounkov polytopes of Schubert varieties arising from cluster structures Reviewed International journal

    Naoki Fujita, Hironori Oya

    Transactions of the American Mathematical Society, Series B   12   910 - 973   2025.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    The theory of Newton–Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton–Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton–Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima–Zelevinsky polytopes.

    DOI： 10.1090/btran/231

    arXiv

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  • $\mathscr{A}=\mathscr{U}$ for cluster algebras from moduli spaces of $G$-local systems Reviewed International coauthorship International journal

    Tsukasa Ishibashi, Hironori Oya, Linhui Shen

    Advances in Mathematics   431   109256 - 109256   2023.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a
    non-trivial minuscule representation and a connected marked surface $\Sigma$
    with at least two marked points and no punctures, we prove that the cluster
    algebra $\mathscr{A}_{\mathfrak{g},\Sigma}$ associated with the pair
    $(\mathfrak{g},\Sigma)$ coincides with the upper cluster algebra
    $\mathscr{U}_{\mathfrak{g},\Sigma}$. The proof is based on the fact that the
    function ring $\mathcal{O}(\mathcal{A}^\times_{G,\Sigma})$ of the moduli space
    of decorated twisted $G$-local systems on $\Sigma$ is generated by matrix
    coefficients of Wilson lines introduced in [IO20]. As an application, we prove
    that the Muller-type skein algebras $\mathscr{S}_{\mathfrak{g},
    \Sigma}[\partial^{-1}]$ [Mul16, IY21, IY] for $\mathfrak{g}=\mathfrak{sl}_2,
    \mathfrak{sl}_3,$ or $\mathfrak{sp}_4$ are isomorphic to the cluster algebras
    $\mathscr{A}_{\mathfrak{g}, \Sigma}$.

    DOI： 10.1016/j.aim.2023.109256

    arXiv

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    Other Link： http://arxiv.org/pdf/2202.03168

  • Wilson lines and their Laurent positivity Reviewed

    Tsukasa Ishibashi, Hironori Oya

    Mathematische Zeitschrift   305 ( 34 )   2023.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    Abstract

    For a marked surface $$\Sigma $$ and a semisimple algebraic group G of adjoint type, we study the Wilson line morphism $$g_{[c]}:{\mathcal {P} }_{G,\Sigma } \rightarrow G$$ associated with the homotopy class of an arc c connecting boundary intervals of $$\Sigma $$, which is the comparison element of pinnings via parallel-transport. The matrix coefficients of the Wilson lines give a generating set of the function algebra $$\mathcal {O}({\mathcal {P} }_{G,\Sigma })$$ when $$\Sigma $$ has no punctures. The Wilson lines have the multiplicative nature with respect to the gluing morphisms introduced by Goncharov–Shen [18], hence can be decomposed into triangular pieces with respect to a given ideal triangulation of $$\Sigma $$. We show that the matrix coefficients $$c_{f,v}^V(g_{[c]})$$ give Laurent polynomials with positive integral coefficients in the Goncharov–Shen coordinate system associated with any decorated triangulation of $$\Sigma $$, for suitable f and v.

    DOI： 10.1007/s00209-023-03355-x

    arXiv

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    Other Link： https://link.springer.com/article/10.1007/s00209-023-03355-x/fulltext.html

  • Isomorphisms among quantum Grothendieck rings and propagation of positivity Reviewed International coauthorship

    Ryo Fujita, David Hernandez, Se-jin Oh, Hironori Oya

    Journal für die reine und angewandte Mathematik (Crelles Journal)   2022 ( 785 )   117 - 185   2022.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter GmbH  

    Abstract

    Let (𝔤,𝗀){\mathfrak{g},\mathsf{g})} be a pair of complex finite-dimensional simple Lie algebras whoseDynkin diagrams are related by (un)folding, with 𝗀{\mathsf{g } } being of simply-laced type.We construct a collection of ring isomorphismsbetween the quantum Grothendieck ringsof monoidal categories 𝒞𝔤{\mathscr{C}_{\mathfrak{g } } } and 𝒞𝗀{\mathscr{C}_{\mathsf{g } } } offinite-dimensional representations over the quantum loop algebras of 𝔤{\mathfrak{g } } and 𝗀{\mathsf{g } }, respectively.As a consequence, we solve long-standing problems: the positivity of the analogs of Kazhdan–Lusztig polynomialsand the positivity of the structure constants of the quantum Grothendieck rings for any non-simply-laced 𝔤{\mathfrak{g } }. In addition, comparing our isomorphisms with the categorical relationsarising from the generalized quantum affine Schur–Weyl dualities, we prove the analog of Kazhdan–Lusztig conjecture(formulated in [D. Hernandez, Algebraic approach to q,tq,t-characters,Adv. Math. 187 2004, 1, 1–52])for simple modules in remarkable monoidal subcategories of 𝒞𝔤{\mathscr{C}_{\mathfrak{g } } } for any non-simply-laced 𝔤{\mathfrak{g } }, and forany simple finite-dimensional modules in 𝒞𝔤{\mathscr{C}_{\mathfrak{g } } } for 𝔤{\mathfrak{g } } of type Bn{\mathrm{B}_{n } }.In the course of the proof we obtain and combine several new ingredients. In particular, we establish a quantum analog of T-systems,and also we generalize the isomorphisms of [D. Hernandez and B. Leclerc,Quantum Grothendieck rings and derived Hall algebras,J. reine angew. Math. 701 2015, 77–126, D. Hernandez and H. Oya,Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan–Lusztig algorithm,Adv. Math. 347 2019, 192–272] to all 𝔤{\mathfrak{g } } in a unified way, that is, isomorphisms between subalgebras of the quantum group of 𝗀{\mathsf{g } } and subalgebras of the quantum Grothendieck ring of 𝒞𝔤{\mathscr{C}_{\mathfrak{g } } }.

    DOI： 10.1515/crelle-2021-0088

    arXiv

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    Other Link： https://www.degruyter.com/document/doi/10.1515/crelle-2021-0088/pdf

  • Cluster realizations of Weyl groups and higher Teichmüller theory Reviewed

    Rei Inoue, Tsukasa Ishibashi, Hironori Oya

    Selecta Mathematica. New Series   27 ( 3 )   2021.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00029-021-00630-9

    arXiv

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    Other Link： https://link.springer.com/article/10.1007/s00029-021-00630-9/fulltext.html

  • Twist automorphisms on quantum unipotent cells and dual canonical bases Reviewed

    Yoshiyuki Kimura, Hironori Oya

    International Mathematics Research Notices. IMRN   2021 ( 9 )   6772 - 6847   2021.5

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1093/imrn/rnz040

    arXiv

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  • Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm Reviewed

    David Hernandez, Hironori Oya

    Advances in Mathematics   347   192 - 272   2019.4

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.aim.2019.02.024

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  • The Chamber Ansatz for quantum unipotent cells Reviewed

    Hironori Oya

    Transformation Groups   24 ( 1 )   193 - 217   2019.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00031-018-9500-y

    arXiv

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  • Quantum Twist Maps and Dual Canonical Bases Reviewed

    Yoshiyuki Kimura, Hironori Oya

    Algebras and Representation Theory   21 ( 3 )   589 - 604   2018.6

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s10468-017-9729-5

    Web of Science

    Scopus

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  • Representations of quantized coordinate algebras via PBW-type elements Reviewed

    Hironori Oya

    Osaka Journal of Mathematics   55 ( 1 )   71 - 115   2018.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    Web of Science

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  • A comparison of Newton-Okounkov polytopes of Schubert varieties Reviewed

    Naoki Fujita, Hironori Oya

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   96 ( 1 )   201 - 227   2017.8

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1112/jlms.12059

    Web of Science

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Books

  • 数理科学 特集：「量子群の世界」(in Japanese)

    Hironori OYA（ Role： Contributor量子ループ代数の有限次元表現論）

    SAIENSU-SHA Co.,Ltd.  2025.3 

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    Total pages：100   Responsible for pages：36--42   Language：Japanese  

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MISC

  • Integral cluster structures on quantized coordinate rings

    Hironori Oya, Fan Qin, Milen Yakimov

    2025.12

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    Language：English  

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    Other Link： https://arxiv.org/pdf/2512.05228

  • 【Book review】Tomoki Nakanishi『団代数論の基礎』 Invited

    Hironori OYA

    数学セミナー(日本評論社)   64 ( 10 )   93 - 93   2025.10

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    Authorship：Lead author   Language：Japanese   Publishing type：Book review, literature introduction, etc.  

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  • Isomorphisms among quantum Grothendieck rings and cluster algebras

    Ryo Fujita, David Hernandez, Se-jin Oh, Hironori Oya

    2023.4

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    Language：English  

    We establish a cluster theoretical interpretation of the isomorphisms of
    [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of
    representations of quantum loop algebras. Consequently, we obtain a
    quantization of the monoidal categorification theorem of
    [Kashiwara-Kim-Oh-Park, arXiv:2103.10067]. We establish applications of these
    new ingredients. First we solve long-standing problems for any non-simply-laced
    quantum loop algebras: the positivity of $(q,t)$-characters of all simple
    modules, and the analog of Kazhdan-Lusztig conjecture for all reachable modules
    (in the cluster monoidal categorification). We also establish the conjectural
    quantum $T$-systems for the $(q,t)$-characters of Kirillov-Reshetikhin modules.
    Eventually, we show that our isomorphisms arise from explicit birational
    transformations of variables, which we call substitution formulas. This reveals
    new non-trivial relations among $(q, t)$-characters of simple modules.

    arXiv

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    Other Link： http://arxiv.org/pdf/2304.02562

  • 【Book review】Toshiki Nakashima『結晶基底と幾何結晶 : 量子群からトロピカルな世界へ』 Invited

    Hironori OYA

    数理科学(サイエンス社)   58 ( 5 )   65 - 65   2020.5

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    Authorship：Lead author   Language：Japanese   Publishing type：Book review, literature introduction, etc.  

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  • 柏原正樹氏京都賞受賞記念座談会(2) Invited

    数学セミナー(日本評論社)   58 ( 10 )   46 - 51   2019.10

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    Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • 柏原正樹氏京都賞受賞記念座談会(1) Invited

    数学セミナー(日本評論社)   58 ( 9 )   44 - 51   2019.9

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    Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • Quantum twist maps and dual canonical bases (表現論と非可換調和解析をめぐる諸問題)

    大矢 浩徳

    数理解析研究所講究録   ( 2031 )   94 - 106   2017.5

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    Language：Japanese   Publisher：京都大学数理解析研究所  

    CiNii Books

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori Oya

    2015.1

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    Publishing type：Internal/External technical report, pre-print, etc.  

    Let $G$ be a connected simply-connected simple complex algebraic group and
    $\mathfrak{g}$ the corresponding simple Lie algebra. In the first half of the
    present paper, we study the relation between the positive part
    $U_q(\mathfrak{n^+})$ of the quantized enveloping algebra $U_q(\mathfrak{g})$
    and the specific irreducible representations of the quantized function algebra
    $\mathbb{Q}_q[G]$, taking into account the right $U_q(\mathfrak{g})$-algebra
    structure of $\mathbb{Q}_q[G]$. This work is motivated by Kuniba, Okado and
    Yamada's result together with Tanisaki and Saito's results. In the latter half,
    we calculate the transition matrices from the canonical basis to the PBW bases
    of $U_q(\mathfrak{n^+})$ using the above relation. Consequently, we show that
    the constants arising from our calculation are described by the structure
    constants for the comultiplication of $U_q(\mathfrak{g})$. In particular, when
    $\mathfrak{g}$ is of type $ADE$, this result implies the positivity of the
    transition matrices, which was originally proved by Lusztig in the case when
    the PBW bases are associated with the adapted reduced words of the longest
    element of the Weyl group, and by Kato in arbitrary cases. In fact, the
    constants in our calculation coincide with ones arising from the calculation
    using the bilinear form on $U_q(\mathfrak{n}^{\pm})$. We explain this
    coincidence in Appendix.

    arXiv

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Presentations

  • A study on the generators of the (quantized) coordinate rings of simple algebraic groups and its applications Invited

    Hironori Oya

    Algebra seminar in South Osaka  2026.2  Osaka Metropolitan University

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    Event date： 2026.2

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：Osaka Metropolitan University   Country：Japan  

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  • A study on the generators of the (quantized) coordinate rings of simple algebraic groups and its applications Invited International conference

    Hironori Oya

    Quantum groups, Monoidal Categorification and Related Topics  2025.12  QSMS Center for Quantum Structures in Modules and Spaces

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    Event date： 2025.12

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Jeju Island   Country：Korea, Republic of  

    File： 18-4 Hironori Oya.pdf

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  • Schur-Weyl双対性 --表現論の世界に橋を架ける-- (Japanese)

    Hironori Oya

    現代数学レクチャーシリーズ 2025  2025.3  Institute of Science Tokyo, School of Science，株式会社すうがくぶんか

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    Event date： 2025.3

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Country：Japan  

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    Other Link： https://youtu.be/i9QxxpjHXAg?si=u3bYYG_RKfXE6mUz

  • Algebraic study of quantum configuration spaces of decorated flags Invited International conference

    Hironori Oya

    Conference on Algebraic Representation Theory (CART) 2024  2024.12  Seoul National University

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    Event date： 2024.12

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Seoul National University   Country：Korea, Republic of  

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  • Non-trivial birational transformations for the q-characters of representations of quantum affine algebras Invited

    Hironori Oya

    Colloquium in Department of Mathematics  2024.4  Tokyo University of Science

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    Event date： 2024.4

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：Tokyo University of Science   Country：Japan  

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  • 幾何構造に代数構造を見る (Japanese)

    Hironori Oya

    現代数学レクチャーシリーズ 2023  2023.9  Tokyo Institute of Technology, School of Science，株式会社すうがくぶんか

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    Event date： 2023.9

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Country：Japan  

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  • Relations among the $q$-characters of simple modules over quantum loop algebras of several Dynkin types Invited International conference

    Hironori Oya

    Integrable Systems and Quantum Groups —In Honor of Masato Okado's 60th Birthday—  2023.3  Osaka Metropolitan University

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    Event date： 2023.3

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Osaka Metropolitan University   Country：Japan  

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  • Application of cluster structures to the representation theory of quantum loop algebras Invited

    Hironori Oya

    The 18th Algebra-Analysis-Geometry Seminar  2023.2  Zoom (online)

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    Event date： 2023.2

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：Zoom (online)   Country：Japan  

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  • Isomorphisms among quantum Grothendieck rings and their applications Invited International conference

    Hironori Oya

    Representation theory and geometry of loop spaces  2023.1  Laboratoire de Mathématiques d'Orsay

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    Event date： 2023.1

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Laboratoire de Mathématiques d'Orsay   Country：France  

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  • Wilson lines on the moduli space of $G$-local systems on a marked surface Invited

    Hironori Oya

    Geometry, Algebra and Physics Seminar at KIAS  2022.12  KIAS (online)

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    Event date： 2022.12

    Language：English   Presentation type：Oral presentation (general)  

    Venue：KIAS (online)   Country：Korea, Republic of  

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  • Wilson lines on the moduli space of decorated twisted $G$-local systems on a marked surface Invited International conference

    Hironori Oya

    Conference on Algebraic Representation Theory 2022 (CART 2022)  2022.11  University of Tsukuba

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    Event date： 2022.11

    Language：English   Presentation type：Oral presentation (general)  

    Venue：University of Tsukuba   Country：Japan  

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  • Application of cluster structures to representation theory of quantum loop algebras

    Hironori Oya

    Ookayama Colloquium  2022.11  Tokyo Institute of Technology

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    Event date： 2022.11

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：Tokyo Institute of Technology   Country：Japan  

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    Other Link： http://www.math.titech.ac.jp/~jimu/colloquium/abstract/R04(2022)/Oya1114.pdf

  • Isomorphisms among quantum Grothendieck rings and their applications

    Hironori Oya

    82nd Colloquium in Department of Mathematical Sciences  2022.7  Shibaura Institute of Technology

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    Event date： 2022.7

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：Shibaura Institute of Technology   Country：Japan  

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  • Isomorphisms among quantum Grothendieck rings and their applications Invited International conference

    Hironori Oya

    Quantum Groups and Cluster Algebras  2022.2  QSMS

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    Event date： 2022.2

    Language：English   Presentation type：Oral presentation (general)  

    Country：Korea, Republic of  

    File： Oya_QGCA.pdf

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  • Isomorphisms among quantum Grothendieck rings and their applications Invited

    Hironori Oya

    Infinite Analysis 21 Workshop Around Cluster Algebras  2021.9  Zoom (online)

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    Event date： 2021.9

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Zoom (online)   Country：Japan  

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  • Twist maps and their applications Invited

    Hironori OYA

    Invited talk in Infinite Analysis Special Session at MSJ Autumn Meeting 2021  2021.9  Chiba University (online)

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    Event date： 2021.9

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：Chiba University (online)   Country：Japan  

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  • Survey of ``Reductive groups, the loop Grassmannian, and the Springer resolution'' by P. Achar and S. Riche

    Hironori Oya

    Workshop on representation theory of reductive algebraic groups  Zoom (online)

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    Event date： 2021.8

    Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Venue：Zoom (online)   Country：Japan  

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  • Algebraic study of quantum configuration spaces of decorated flags Invited

    Hironori OYA

    Séminaire d'Algèbre  2025.4  Institut Henri Poincaré

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    Language：English   Presentation type：Oral presentation (general)  

    Venue：Institut Henri Poincaré   Country：France  

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  • Twist automorphisms on quantum unipotent cells and the Chamber Ansatz

    Hironori OYA

    Algebraic Lie Theory and Representation Theory 2017  2017.6  Shizuoka

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    Presentation type：Oral presentation (general)  

    Venue：Shizuoka  

    File： oya_ALTReT2017_handout_v2.pdf

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  • Quantum twist automorphisms and quantum Chamber Ansatz formulae for unipotent cells

    Hironori OYA

    Algebraic Analysis and Representation Theory -- In honor of Professor Masaki Kashiwara's 70th Birthday --  2017.6  RIMS

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    Presentation type：Poster presentation  

    Venue：RIMS  

    File： oya_Kashiwara70_poster_v2.pdf

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  • Quantum twist maps and dual canonical bases Invited

    Hironori OYA

    Tsukuba Freshman Seminar  2016.6  University of Tsukuba

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    Presentation type：Oral presentation (general)  

    Venue：University of Tsukuba  

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  • Quantum twist maps and dual canonical bases

    Hironori OYA

    Various Issues relating to Representation Theory and Non-commutative Harmonic Analysis  2016.6  RIMS

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    Presentation type：Oral presentation (general)  

    Venue：RIMS  

    File： oya_RIMS2016_handout.pdf

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  • Twist maps on quantum unipotent cells and the Chamber Ansatz

    Hironori OYA

    Oberseminar Algebra  2016.10  Universität zu Köln

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    Presentation type：Oral presentation (general)  

    Venue：Universität zu Köln  

    File： oya_Cologne2016_handout.pdf

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  • Quantum twist automorphisms and the Chamber Ansatz

    Hironori OYA

    Langlands and Harmonic Analysis  2017.3  Shizuoka

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    Presentation type：Oral presentation (general)  

    Venue：Shizuoka  

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  • Relations between quantum groups and quivers via Hall algebras (survey) Invited

    Hironori OYA

    Graduate Student Colloquium  2015.10  Osaka City University

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    Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Venue：Osaka City University  

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  • Representations of quantized coordinate algebras via PBW-type elements

    Hironori OYA

    Kobe Seminar on Integrable Systems  2016.1  Kobe University

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    Presentation type：Oral presentation (general)  

    Venue：Kobe University  

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  • Langlands duality for representations of quantum groups and quantum Frobenius maps (survey)

    Hironori OYA

    Langlands and Harmonic Analysis  2016.3  Kyushu University

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    Presentation type：Oral presentation (general)  

    Venue：Kyushu University  

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  • On some reducible representations of the quantized coordinate algebras

    Hironori OYA

    21st Conference on Algebra for Young Researchers in Japan  2016.3  Nara Women's University

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    Presentation type：Oral presentation (general)  

    Venue：Nara Women's University  

    File： oya_21st_wakate.pdf

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori OYA

    Shinshu Algebra Seminar  2015.5  Shinshu University

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    Presentation type：Oral presentation (general)  

    Venue：Shinshu University  

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori OYA

    Algebraic Lie theory and Representation theory 2015  2015.6  Okayama

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    Presentation type：Oral presentation (general)  

    Venue：Okayama  

    File： oya_ALTReT2015.pdf

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases Invited

    Hironori OYA

    Tsukuba Freshman Seminar  2015.7  University of Tsukuba

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    Presentation type：Oral presentation (general)  

    Venue：University of Tsukuba  

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori OYA

    Lie Groups and Representation Theory Seminar  2015.1  The University of Tokyo

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    Presentation type：Oral presentation (general)  

    Venue：The University of Tokyo  

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori OYA

    Representation Theory Seminar  2015.2  RIMS

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    Presentation type：Oral presentation (general)  

    Venue：RIMS  

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  • Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases

    Hironori OYA

    Algebra Seminar  2015.2  Osaka City University

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    Presentation type：Oral presentation (general)  

    Venue：Osaka City University  

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  • The representations of quantized function algebras and the transition matrices between Canonical bases and PBW bases

    Hironori OYA

    MSJ Spring Meeting 2015  2015.3  Meiji University

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    Presentation type：Oral presentation (general)  

    Venue：Meiji University  

    File： oya_suugakukai2015spring.pdf

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  • A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$

    Hironori OYA

    Algebra Seminar  2014.1  Osaka City University

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    Presentation type：Oral presentation (general)  

    Venue：Osaka City University  

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  • A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$

    Hironori OYA

    19th Conference on Algebra for Young Researchers in Japan  2014.2  Shinshu University

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    Presentation type：Oral presentation (general)  

    Venue：Shinshu University  

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  • A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$

    Hironori OYA

    17th Conference on Representation Theory of Algebraic Groups and Quantum Groups  2014.6  Toyama

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    Presentation type：Oral presentation (general)  

    Venue：Toyama  

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  • Systematic construction of isomorphisms among quantum Grothendieck rings Invited

    Hironori OYA

    Representation Theory Seminar  2021.2  RIMS

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    Language：English   Presentation type：Oral presentation (general)  

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  • Similarities in representation theory of quantum affine algebras of several different Dynkin types International conference

    Hironori OYA

    The 3rd UOG-SIT Workshop in Pure/Applied Mathematics and Computer Science  2019.3  University of Guam

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    Language：English   Presentation type：Oral presentation (general)  

    Venue：University of Guam  

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  • Calculation of the q-characters of simple modules over quantum loop algebras of non-symmetric type Invited

    Hironori OYA

    The 64th Algebra Symposium  2019.9  Tohoku University

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    Presentation type：Oral presentation (general)  

    Venue：Tohoku University  

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  • Cluster algebras and calculation of q-characters of simple modules over quantum loop algebras of non-symmetric type Invited International conference

    Hironori OYA

    Representation Theory of Algebraic Groups and Quantum Groups -- in honor of Professor Ariki's 60th birthday --  2019.10  RIMS

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    Language：English   Presentation type：Oral presentation (general)  

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  • Newton-Okounkov polytopes of Schubert varieties arising from cluster structures and representation-theoretic polytopes Invited

    Hironori OYA

    Séminaire d'Algèbre  2020.5  Institut Henri Poincaré (online)

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    Language：English   Presentation type：Oral presentation (general)  

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B Invited International conference

    Hironori OYA

    Conference on Algebraic Representation Theory 2018  2018.11  Tongji University

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    Language：English   Presentation type：Oral presentation (general)  

    Venue：Tongji University  

    File： oya_CART2018_handout.pdf

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B Invited

    Hironori OYA

    Representation Theory Seminar  2018.12  RIMS

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    Language：English   Presentation type：Oral presentation (general)  

    Venue：RIMS  

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  • Similarities in finite-dimensional representation theory of quantum affine algebras of several different Dynkin types Invited

    Hironori OYA

    Invited talk in Algebra Session at MSJ Spring Meeting 2019  2019.3  Tokyo Institute of Technology

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    Presentation type：Oral presentation (invited, special)  

    Venue：Tokyo Institute of Technology  

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B

    Hironori OYA

    Séminaire de Théorie des Groupes  2018.6  Lamfa - Université de Picardie Jules Verne

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    Presentation type：Oral presentation (general)  

    Venue：Lamfa - Université de Picardie Jules Verne  

    File： oya_Amiens2018_handout.pdf

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B

    Hironori OYA

    Oberseminar Algebra  2018.6  Universität zu Köln

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    Presentation type：Oral presentation (general)  

    Venue：Universität zu Köln  

    File： oya_Cologne_handout.pdf

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  • Similarities in the finite-dimensional representation theory for quantum affine algebras of several different types

    Hironori OYA

    72nd Colloquium in Department of Mathematical Sciences  2018.10  Shibaura Institute of Technology

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    Presentation type：Oral presentation (general)  

    Venue：Shibaura Institute of Technology  

    File： oya_shibauraColloquium_handout.pdf

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  • Cluster realizations of Weyl groups and their application

    Hironori OYA

    Algebra seminar in South Osaka  2018.10  I-site Namba

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    Presentation type：Oral presentation (general)  

    Venue：I-site Namba  

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  • The Chamber Ansatz formulae for quantum unipotent cells

    Hironori OYA

    Representation Theory Seminar  2017.7  RIMS

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    Presentation type：Oral presentation (general)  

    Venue：RIMS  

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  • Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells

    Hironori OYA

    Séminaire d'Algèbre  2017.10  Institut Henri Poincaré

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    Presentation type：Oral presentation (general)  

    Venue：Institut Henri Poincaré  

    File： oya_Parisalg_handout_v2.pdf

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B

    Hironori OYA

    Séminaire Groupes, Représentations et Géométrie  2018.3  Bâtiment Sophie Germain

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    Presentation type：Oral presentation (general)  

    Venue：Bâtiment Sophie Germain  

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  • Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B

    Hironori OYA

    Algebraic Lie Theory and Representation Theory 2018  2018.5  Nagano

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    Presentation type：Oral presentation (general)  

    Venue：Nagano  

    File： oya_ALTReT2018_handout.pdf

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  • Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells Invited

    Hironori OYA

    Tsukuba Workshop on Pure and Applied Mathematics 2017  2017.7  University of Tsukuba

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    Presentation type：Oral presentation (general)  

    Venue：University of Tsukuba  

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  • Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells

    Hironori OYA

    Ring Theory and Representation Theory Seminar  2017.7  Nagoya University

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    Presentation type：Oral presentation (general)  

    Venue：Nagoya University  

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▼display all

Awards

  • Reiwa 5th year Rigakuin Wakate Kenkyu Shoreisho "令和5年度理学院若手研究奨励賞"

    2023.12   Tokyo Institute of Technology  

    Hironori Oya

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  • Dean's Prize

    2017.3   Graduate School of Mathematical Sciences, The University of Tokyo  

    Hironori OYA

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  • Dean's Prize

    2014.3   Graduate School of Mathematical Sciences, The University of Tokyo  

    Hironori OYA

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Research Projects

  • 量子ループ代数の表現圏に見られる類似構造とその発展

    Grant number：23K12950  2023.4 - 2027.3

    日本学術振興会  科学研究費助成事業 若手研究  若手研究

    大矢 浩徳

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    Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）

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  • Investigation of similarities in representation theory of quantum affine algebras of several different Dynkin types

    Grant number：19K14515  2019.4 - 2023.3

    Japan Society for the Promotion of Science  Grant-in-Aid for Early-Career Scientists  Grant-in-Aid for Early-Career Scientists

    Hironori OYA

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    Authorship：Principal investigator  Grant type：Competitive

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  • 量子座標環を用いた量子包絡環の構造、表現の研究

    2015.4 - 2017.3

    日本学術振興会  特別研究員奨励費 (DC2) 

    大矢 浩徳

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount：\1700000

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Teaching Experience

Academic Activities

  • Science Tokyo Representation Theory Seminar

    Role(s)： Planning, management, etc.

    2024.10

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  • Algebraic Lie Theory and Representation Theory 2023

    Role(s)： Planning, management, etc.

    （ Tokyo Institute of Technology, Ookayama Campus, West Bldg. 9, Collaboration Room ） 2023.5

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    Type：Academic society, research group, etc. 

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  • Tokyo Tech Representation Theory Seminar

    Role(s)： Planning, management, etc.

    2022.12 - 2024.9

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    Type：Academic society, research group, etc. 

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  • Online school : Quantum Geometry and Representation Theory II

    Role(s)： Planning, management, etc.

    （ Online (Zoom) ） 2022.2

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    Type：Academic society, research group, etc. 

    Skein algebras and quantum cluster varieties (quantum Teichmüller spaces) provide quantizations of character varieties for surfaces, and the quantum trace map relates these two approaches. The goal of this online school is to provide an introduction to these research topics and to learn recent progress in these areas.

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  • Online school : Quantum Geometry and Representation Theory

    Role(s)： Planning, management, etc.

    （ Online (Zoom) ） 2021.3

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    Type：Academic society, research group, etc. 

    Since its naissance in the 00s, cluster theory (the theory treating cluster algebras/cluster varieties) has been extensively developed in connection with various fields of mathematics and theoretical physics. In this online school, we will focus on the appearance of cluster theory and its quantization in representation theory of quantum groups and geometry of several moduli spaces.

    The online school consists of 5 intensive lectures and 3 research talks. The goal of the school is to provide a rigorous introduction of these research areas and an opportunity of discussion between young researchers and experts.

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