Hironori OYA

NEXT

Research interests

Kac-Moody Lie algebras, Quantum groups (= quantized enveloping algebras, quantized coordinate algebras) and Quantum cluster algebras

Papers and Preprints

• A note on cluster structure of the coordinate ring of a simple algebraic group, arXiv:2504.09011v1 [pdf] (updated on 11 April 2025)
• Isomorphisms among quantum Grothendieck rings and cluster algebras, joint work with Ryo Fujita, David Hernandez, and Se-jin Oh, arXiv:2304.02562v2 [pdf] (updated on 7 May 2023)
• $\mathscr{A}=\mathscr{U}$ for cluster algebras from moduli spaces of $G$-local systems, joint work with Tsukasa Ishibashi and Linhui Shen, Adv. Math. 431 (2023), Paper No. 109256, 50 pp. (website), arXiv:2202.03168v3 [pdf] (updated on 27 August 2023)
• Isomorphisms among quantum Grothendieck rings and propagation of positivity, joint work with Ryo Fujita, David Hernandez, and Se-jin Oh, J. Reine Angew. Math. 785 (2022), 117--185. (website), arXiv:2101.07489v3 [pdf] (updated on 15 December 2021)
• Wilson lines and their Laurent positivity, joint work with Tsukasa Ishibashi, Math. Z. 305 (2023), 34. (website), arXiv:2011.14260v4 [pdf] (updated on 6 November 2023)
• Newton-Okounkov polytopes of Schubert varieties arising from cluster structures, joint work with Naoki Fujita, arXiv:2002.09912v2 [pdf] (updated on 6 March 2023)
• Cluster realizations of Weyl groups and higher Teichmüller theory, joint work with Rei Inoue and Tsukasa Ishibashi, Selecta Math. (N.S.) 27 (2021), no. 3, Paper No. 37, 84 pp. (website), arXiv:1902.02716v3 [pdf] (updated on 3 February 2021)
• Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm, joint work with David Hernandez, Adv. Math. 347 (2019), 192--272. (website), arXiv:1803.06754v2 [pdf] (updated on 15 February 2019)
• The Chamber Ansatz for quantum unipotent cells, Transform. Groups 24 (2019), no. 1, 193--217. (website), arXiv:1702.00383v2 [pdf] (updated on 23 August 2018)
• Twist automorphisms on quantum unipotent cells and dual canonical bases, joint work with Yoshiyuki Kimura, Int. Math. Res. Not. IMRN 2021, no. 9, 6772--6847. (website), arXiv:1701.02268v4 [pdf] (updated on 13 February 2019)
• A comparison of Newton-Okounkov polytopes of Schubert varieties, joint work with Naoki Fujita, J. Lond. Math. Soc. (2) 96 (2017), no. 1, 201--227. (website), arXiv:1610.08783v2 [pdf] (updated on 24 July 2017)
• Quantum twist maps and dual canonical bases, joint work with Yoshiyuki Kimura, Algebr. Represent. Theory 21 (2018), no. 3, 589--604. (website), arXiv:1604.07748v2 [pdf] (updated on 20 August 2017)
• Representations of quantized coordinate algebras via PBW-type elements, Osaka J. Math. 55 (2018), no. 1, 71--115. (website), [pdf] 【This is a significantly revised version of the preprint ``Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases'' arXiv:1501.01416v3 [pdf] (updated on 6 July 2015).】

Upcoming talks

• TBA, Quantum groups, monoidal categorification and related topics, Korea, December 15--19, 2025.

Past talks

• Algebraic study of quantum configuration spaces of decorated flags, Séminaire d'Algèbre, Institut Henri Poincaré, April 2025.
• Algebraic study of quantum configuration spaces of decorated flags, Conference on Algebraic Representation Theory (CART) 2024, Seoul National University, December 2024.
• 【Intensive Lecture】Introduction to finite-dimensional representation theory of quantum affine algebras, Lectures for Mathematical Sciences A, Waseda University, May 30--31, June 3--5, 2024.
• 【Intensive Lecture】Introduction to cluster algebras, Special Lecture 1, Tokyo University of Science, April 22--26, 2024.
• Non-trivial birational transformations for the $q$-characters of representations of quantum affine algebras, Colloquium in Department of Mathematics, Tokyo University of Science, April 2024.
• Relations among the $q$-characters of simple modules over quantum loop algebras of several Dynkin types, Integrable Systems and Quantum Groups —In Honor of Masato Okado's 60th Birthday—, Osaka Metropolitan University, March 2023.
• Application of cluster structures to the representation theory of quantum loop algebras, The 18th Algebra-Analysis-Geometry Seminar, Zoom (online), February 2023.
• Isomorphisms among quantum Grothendieck rings and their applications, Representation theory and geometry of loop spaces, Laboratoire de Mathématiques d'Orsay, January 2023.
• Wilson lines on the moduli space of $G$-local systems on a marked surface, Geometry, Algebra and Physics Seminar at KIAS, KIAS (online), December 2022.
• Wilson lines on the moduli space of decorated twisted $G$-local systems on a marked surface, Conference on Algebraic Representation Theory (CART) 2022, University of Tsukuba, November 2022.
• 【Intensive Lecture】Representation theory of quantum loop algebras and Cluster algebras, Special lectures on advanced topics in Mathematics B, Tokyo Institute of Technology, November 7--8 and 14--16, 2022.
• Application of cluster structures to representation theory of quantum loop algebras, Ookayama Colloquium, Tokyo Institute of Technology, November 2022.
• Isomorphisms among quantum Grothendieck rings and their applications, 82nd Colloquium in Department of Mathematical Sciences, Shibaura Institute of Technology, July 2022.
• Isomorphisms among quantum Grothendieck rings and their applications, Quantum Groups and Cluster Algebras, QSMS, Seoul, Korea (online), February 2022.
• Isomorphisms among quantum Grothendieck rings and their applications, Infinite Analysis 21 Workshop Around Cluster Algebras, Zoom (online), September 2021.
• Twist maps and their applications, Invited talk in Infinite Analysis Special Session at MSJ Autumn Meeting 2021, Chiba University (online), September 2021.
• Survey of ``Reductive groups, the loop Grassmannian, and the Springer resolution'' by P. Achar and S. Riche , Workshop on representation theory of reductive algebraic groups, Zoom (online), August 2021.
• Systematic construction of isomorphisms among quantum Grothendieck rings, Representation Theory Seminar, RIMS (online), February 2021.
• Newton-Okounkov polytopes of Schubert varieties arising from cluster structures and representation-theoretic polytopes, Séminaire d'Algèbre, Institut Henri Poincaré (online), May 2020.
• Calculation of $q$-characters of simple modules over quantum loop algebras of non-symmetric type, Workshop “Categorifications: Hecke algebras, finite groups and quantum groups”, Institut Henri Poincaré, 23--27 March 2020. (Cancelled due to the outbreak of COVID-19)
• Newton-Okounkov polytopes of Schubert varieties arising from cluster structures and representation-theoretic polytopes, Infinite Analysis 20 (IA20) Workshop: Cluster algebras, representation theory, and geometry, Osaka City University Advanced Mathematical Institute, 2--6 March 2020. (Cancelled due to the outbreak of COVID-19)
Talks before 2020
Cluster algebras and calculation of $q$-characters of simple modules over quantum loop algebras of non-symmetric type, Representation Theory of Algebraic Groups and Quantum Groups -- in honor of Professor Ariki's 60th birthday --, RIMS, October 2019.
Calculation of the $q$-characters of simple modules over quantum loop algebras of non-symmetric type, The 64th Algebra Symposium, Tohoku University, September 2019.
Similarities in representation theory of quantum affine algebras of several different Dynkin types, The 3rd UOG-SIT Workshop in Pure/Applied Mathematics and Computer Science, University of Guam, March 2019.
Similarities in finite-dimensional representation theory of quantum affine algebras of several different Dynkin types, Invited talk in Algebra session at MSJ Spring Meeting 2019, Tokyo Institute of Technology, March 2019.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Representation Theory Seminar, RIMS, December 2018.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Conference on Algebraic Representation Theory 2018 [reference slides], Tongji University, November 2018.
Cluster realizations of Weyl groups and their application, Algebra seminar in South Osaka, I-site Namba, October 2018.
Similarities in the finite-dimensional representation theory for quantum affine algebras of several different types, 72nd Colloquium in Department of Mathematical Sciences [reference slides (typos corrected 12/10/2018)], Shibaura Institute of Technology, October 2018.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Oberseminar Algebra [reference slides], Universität zu Köln, June 2018.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Séminaire de Théorie des Groupes [reference slides (typos corrected 14/06/2018)], Lamfa - Université de Picardie Jules Verne, June 2018.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Algebraic Lie Theory and Representation Theory (ALTReT) 2018 [reference slides (typos corrected 14/06/2018)], Karuizawa, May 2018.
Quantum Grothendieck ring isomorphisms for quantum affine algebras of type A and B, Séminaire Groupes, Représentations et Géométrie, Bâtiment Sophie Germain, March 2018.
Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells, Séminaire d'Algèbre [reference slides (typos corrected 16/10/2017)], Institut Henri Poincaré, October 2017.
The Chamber Ansatz formulae for quantum unipotent cells, Representation Theory Seminar, RIMS, July 2017.
Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells, Ring Theory and Representation Theory Seminar, Nagoya University, July 2017.
Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells, Tsukuba Workshop on Pure and Applied Mathematics 2017, University of Tsukuba, July 2017.
Quantum twist automorphisms and quantum Chamber Ansatz formulae for unipotent cells (poster), Algebraic Analysis and Representation Theory -- In honor of Professor Masaki Kashiwara's 70th Birthday -- [reference poster (typos corrected 16/10/2017)], RIMS, June 2017.
Twist automorphisms on quantum unipotent cells and the Chamber Ansatz, Algebraic Lie Theory and Representation Theory (ALTReT) 2017 [reference slides (typos corrected 16/10/2017)], Shizuoka, June 2017.
(1)Total positivity and cluster algebras (survey), (2) Quantum twist automorphisms and the Chamber Ansatz, Langlands and Harmonic Analysis, Shizuoka, March 2017.
Twist maps on quantum unipotent cells and the Chamber Ansatz, Oberseminar Algebra [reference slides], Universität zu Köln, October 2016.
Quantum twist maps and dual canonical bases, Various Issues relating to Representation Theory and Non-commutative Harmonic Analysis [reference slides], Proceedings: website [pdf(Japanese)], RIMS, June 2016.
Quantum twist maps and dual canonical bases, Tsukuba Freshman Seminar, University of Tsukuba, June 2016.
On some reducible representations of the quantized coordinate algebras, 21st Conference on Algebra for Young Researchers in Japan [reference slides], Nara Women's University, March 2016.
Langlands duality for representations of quantum groups and quantum Frobenius maps (survey), Langlands and Harmonic Analysis, Kyushu University, March 2016.
Representations of quantized coordinate algebras via PBW-type elements, Kobe Seminar on Integrable Systems, Kobe University, January 2016.
Relations between quantum groups and quivers via Hall algebras (survey), Graduate Student Colloquium, Osaka City University Advanced Mathematical Institute, October 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Tsukuba Freshman Seminar, University of Tsukuba, July 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Algebraic Lie theory and Representation theory (ALTReT) 2015 [reference slides], Okayama, June 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Shinshu Algebra Seminar, Shinshu University, May 2015.
The representations of quantized function algebras and the transition matrices between Canonical bases and PBW bases, MSJ Spring Meeting 2015 [reference slides], Meiji University, March 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Algebra Seminar, Osaka City University Advanced Mathematical Institute, February 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Representation Theory Seminar, RIMS, February 2015.
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases, Lie Groups and Representation Theory Seminar, The University of Tokyo, January 2015.
A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$, 17th Conference on Representation Theory of Algebraic Groups and Quantum Groups (RAQ2014) [program pdf], Toyama, June 2014.
A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$, 19th Conference on Algebra for Young Researchers in Japan, Shinshu University, February 2014.
A construction of irreducible representations of the quantized function algebra $\mathbb{C}[SL_n]_v$, Algebra Seminar, Osaka City University Advanced Mathematical Institute, January 2014.

Workshop and seminar organization

• Informal Learning Seminar on Quantum Groups and Related Topics , Tokyo Institute of Technology, December 2022--.
• Science Tokyo Representation Theory Seminar , Institute of Science Tokyo, October 2024--.
• Tokyo Tech Representation Theory Seminar , Tokyo Institute of Technology, December 2022-- September 2024.
• Spring School on Cluster Algebras 2025 , Nagoya University, February 24--26, 2025.
• Combinatorial Representation Theory and Geometry ---In Honor of Satoshi Naito's 60th Birthday--- , Tokyo Institute of Technology, June 24--28, 2024.
• Advances in Cluster Algebras (ACA) 2024 , Nagoya University, March 11--13, 2024.
• Summer School on Cluster Algebras 2023 , Online Zoom, August 21--23, 2023.
• Algebraic Lie Theory and Representation Theory (ALTReT) 2023 , Tokyo Institute of Technology (Hybrid), May 11--15, 2023.
• Advances in Cluster Algebras (ACA) 2023 , Online Zoom, March 22--24, 2023.
• Trends in Cluster Algebras (TCA) 2022 , Online Zoom, September 20--22, 2022.
• Online school : Quantum Geometry and Representation Theory II , Online Zoom, February 12--14, 2022.
• Online school : Quantum Geometry and Representation Theory , Online Zoom, March 1--5, 2021.

Editorial work

• Kodai Mathematical Journal

Last updated on April 15, 2025.