Rchr
J-GLOBAL ID：200901093297244007
Update date: Aug. 11, 2024
Toshiki Nakashima
ナカシマ トシキ | Toshiki Nakashima
Affiliation and department：
Job title：
Professor
Research field (1)：
Algebra
Research keywords (5)：
Quantum group
, crystal base
, geometric crystal
, Cluster algebra
, categorification
Research theme for competitive and other funds (21)：
- 2020 - 2025 幾何結晶とクラスター代数への結晶基底からのアプローチ
- 2015 - 2020 クラスター代数と結晶基底の表現論的研究
- 2011 - 2016 Representation theory of Iwahori-Hecke algebras and reflection groups
- 2010 - 2015 Algebraic analysis of infinite symmetry
- 2010 - 2015 幾何結晶上のトロピカルR写像の構成と結晶基底への応用
- 2009 - 2012 Representation of finite groups, character sums, and their applications
- 2007 - 2010 アファイン幾何結晶の構成と結晶基底の表現論
- 2008 - 2010 Representation Theory of Quantum Groups and Integrable Systems
- 2006 - 2009 Algebraic Analysis of Infinite Symmetry
- 2006 - 2008 Representations of finite reductive groups and applications
- 2004 - 2007 量子群と幾何結晶の区分線形的表現論
- 2001 - 2004 量子群の組合せ論的表現論
- 2002 - 2004 A Study on the zeta functions attached with the irreducible representations of finite reductive groups
- 2001 - 2004 Algebraic Analysis of Representation Theory
- 2000 - 2001 Study on representations of algebraic groups and finite groups, and applications
- 1997 - 2000 Algebraic analysis of representation theory
- 1997 - 1999 変形された量子展開環の結晶基底について
- 1997 - 1999 Studies on Representations of Finite Groups and Applications
- 1997 - 1998 Combinatorial Studies of Demazure Modules
- 1996 - 1997 柏原代数の頂点作用素とトレースについて
- 1994 - 1995 柏原代数に付随するq-頂点作用素のN点関数について
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Papers (59)：
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Toshiki Nakashima. Geometric crystal on unipotent variety. Proceedings of Symposia in Pure Mathematics. 2024. 108. 465-481
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Yuki Kanakubo, Gleb Koshevoy, Toshiki Nakashima. An Algorithm for Berenstein-Kazhdan Decoration Functions and Trails for Classical Lie Algebras. International Mathematics Research Notices. 2024. 2024. 4. 3223-3277
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YUKI KANAKUBO, TOSHIKI NAKASHIMA. HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS. Transformation Groups. 2023. 28. 1. 327-373
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Yuki Kanakubo, Gleb Koshevoy, Toshiki Nakashima. An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations. Journal of Algebra. 2022. 608. 106-142
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T.Nakashima (with, Y.Kanakubo. Explicit forms of polyhedral realizations of crystal bases associated with adapted sequences. Toyama Mathematical Journal. 2021. 42. 1-28
ｍore...
MISC (8)：
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Toshiki Nakashima. A survey on categorified crystal structure on localized quantum coordinate rings. RIMS Kôkyûroku. 2023. 2258. 20-36
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Toshiki Nakashima. CRYSTAL STRUCTURE ON LOCALIZED QUANTUM COORDINATE RINGS. RIMS Kôkyûroku. 2022. 2234
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中島 俊樹. 団代数と結晶基底 (特集 団代数をめぐって : 新たな共通構造の認識). 数理科学. 2015. 53. 3. 21-26
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柏原 正樹, 中島 俊樹, 尾角 正人. 幾何クリスタルと可積分系(可積分系数理の眺望). 数理解析研究所講究録. 2007. 1541. 150-165
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中島俊樹. 書評 J. Hong and S.-J. Kang: Introduction to Quantum Groups and Crystal Bases (Grad. Stud. Math., 42). 数学. 2006. 58. 1. 102-111
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Books (6)：
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『結晶基底と幾何結晶』臨時別冊・数理科学SGCライブラリ148
サイエンス社 2019
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数理科学、団代数と結晶基底 (特集 団代数をめぐって : 新たな共通構造の認識)
サイエンス社 2015
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数学セミナー、量子群と結晶基底 (特集 図形から学ぶリー代数)
日本評論社 2009
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『Algebraic analysis and around : in honor of professor Masaki Kashiwara's 60th birthday』 (Advanced studies in pure mathematics, 54)
Mathematical Society of Japan 2009 ISBN:9784931469518
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書評 J. Hong and S.-J. Kang: Introduction to Quantum Groups and Crystal Bases (Grad. Stud. Math., 42)
日本数学会 2006
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Lectures and oral presentations (39)：
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Presentation of Crystal bases
(Crystal Bases and Then ... 2024)
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Localized Quantum Unipotent Coordinate Category and Cellular Crystals
(Combinatorial Representation Theory and Geometry 2024)
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Categorified Crystal Bases on Localized Quantum Coordinate Rings and Cellular Crystals
(Combinatorics and Arithmetic for Physics 2023)
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Crystal bases and Application to Combinatorics of Young tableaux
(Math SWU seminar 2023)
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Crystal bases and Littlewood-Richardson rules
(Math CU seminar 2023)
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Education (2)：
- 1988 - 1992 Kyoto University
- 1984 - 1988 The University of Tokyo Faculty of Science
Professional career (1)：
Association Membership(s) (1)：
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