NAKASHIMA Toshiki 中島俊樹

… Alternative Names

Researcher Number	60243193
Other IDs
Affiliation (Current)	2018 : 上智大学, 理工学部, 教授
Affiliation (based on the past Project Information) *help	2004 – 2017 : Sophia University, Faculty of Science and Technology, Professor, 理工学部, 教授 2001 – 2004 : Faculty of Science and Technology, Sophia University, Associate Professor, 理工学部, 助教授 1998 – 2001 : Sophia Univ.College of Sci.& Tech.L, 理工学部, 講師 1997 : 大阪大学, 大学院・基礎工学研究科, 助手 1996 : 大阪大学, 基礎工学部, 助手 1994 : 大阪大学, 基礎工学部, 助手
Review Section/Research Field	Principal Investigator Algebra / Algebra Except Principal Investigator Algebra / Algebra
Keywords	Principal Investigator 結晶基底 / 量子群 / 幾何結晶 / ヘッケ環 / 多面体表示 / 超離散化 / 表現論 / 代数群 / クラスター代数 / 頂点作用素 … More Except Principal Investigator 量子群 / Gelfand-Graev representation / character sum / 表現論 / coinvariant algebra / Kloosterman sum / ガウス和 / Gauss sum / 結晶基底 / 有限群の表現論 / Hilbert scheme of G-orbit / 指標和 / gaussian sum / unitary Kloosterman sum / アフィンリー環 / 変形量子化 / representation theory / Hilbert scheme of G-orbits / 可解模型 / McKay correspondence / 有限群の表現 / 表現 / 有限群 / D-加群 / finite group / combinatorics / 代数学 / algebraic group / almost character / セルオートマトン / 偏屈層 / general linear group / 有限簡約代教群 / ゲルファンドーグラエフ表現 / 代数解析 / 余不変式環 / McKay corresondence / quantum groups / 指標 / Character sum / アフィンリ一環 / D-modules / 箙ヘッケ環 / 組み合せ論 / unitary kloosterman sum / affine Lie Algebra / 岩堀ヘッケ環 / quantum group / 旗多様体 / 代数 / 特殊凾数 / イタリア：フランス：アメリカ：韓国 / 対称空間 / ゼータ関数 / クルースタマン和 / Gelfand-Gracv representation / ヒルベルトスキーム / 一般線型群 / 中単指標 / 量子郡 / 圏化 / 既約表現 / ストリングC群 / 有限簡約群 / finite reductive groups / 可積分系 / クルスターマン和 / guantum group / solvable models / 鏡映群 / McKay correspndence / 幾何学的表現論 / 群論 / kloosterman sum / irreducible representation / 組み合わせ論 / マルコフトレース / 簡約代数群 / 超局所解析 / ヘッケ環 / アフィンヘッケ環 / 不確定特異点ホロノミック系 / SL(3,C)の有限部分群 / ヤン・バクスター方程式 / Gelfand-Graev表現 / 国際研究者交流 / crystal bases / zeta function / ワイル・シューア双対性 / 有限簡約代数群 / 組合せ論 / 組み合わせ / リーマン・ヒルベルト対応 Less

クラスター代数と結晶基底の表現論的研究Principal InvestigatorOngoing
- Principal Investigator
  
  中島俊樹
- Project Period (FY)
  2015 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Representation theory of Iwahori-Hecke algebras and reflection groups
- Principal Investigator
  
  Gomi Yasushi
- Project Period (FY)
  2011 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Algebraic analysis of infinite symmetry
- Principal Investigator
  
  KASHIWARA Masaki
- Project Period (FY)
  2010 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Kyoto University
Construction of tropical R maps on geometric crystals and its applications to crystal basesPrincipal Investigator
- Principal Investigator
  
  NAKASHIMA Toshiki
- Project Period (FY)
  2010 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Representation of finite groups, character sums, and their applications
- Principal Investigator
  
  SHINODA Ken-ichi
- Project Period (FY)
  2009 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Representation Theory of Quantum Groups and Integrable Systems
- Principal Investigator
  
  OKADO Masato
- Project Period (FY)
  2008 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Osaka University
Construction of affine geometric crystals and Representation theory of crystal basesPrincipal Investigator
- Principal Investigator
  
  NAKASHIMA Toshiki
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Algebraic Analysis of Infinite Symmetry
- Principal Investigator
  
  KASHIWARA Masaki
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Kyoto University
Representations of finite reductive groups and applications
- Principal Investigator
  
  SHINODA Ken-ichi
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Piecewise Linear Representation Theory of Quantum Groups and Geometric CrystalsPrincipal Investigator
- Principal Investigator
  
  NAKASHIMA Toshiki
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
A Study on the zeta functions attached with the irreducible representations of finite reductive groups
- Principal Investigator
  
  SHINODA Ken-ichi
- Project Period (FY)
  2002 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Algebraic Analysis of Representation Theory
- Principal Investigator
  
  KASHIWARA Masaki
- Project Period (FY)
  2001 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  KYOTO UNIVERSITY
Combinatorial Representation Theory of Quantum GroupsPrincipal Investigator
- Principal Investigator
  
  NAKASHIMA Toshiki
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
Study on representations of algebraic groups and finite groups, and applications
- Principal Investigator
  
  SHINODA Ken-ichi
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
変形された量子展開環の結晶基底についてPrincipal Investigator
- Principal Investigator
  
  中島俊樹
- Project Period (FY)
  1998
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
  Osaka University
Algebraic analysis of representation theory
- Principal Investigator
  
  KASHIWARA Masaki
- Project Period (FY)
  1997 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (A).
- Research Field
  
  Algebra
- Research Institution
  KYOTO UNIVERSITY, RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES
Combinatorial Studies of Demazure Modules
- Principal Investigator
  
  OKADO Masato
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Osaka University
Studies on Representations of Finite Groups and Applications
- Principal Investigator
  
  SHINODA Ken-ichi
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Sophia University
柏原代数の頂点作用素とトレースについてPrincipal Investigator
- Principal Investigator
  
  中島俊樹
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Osaka University
柏原代数に付随するq-頂点作用素のN点関数についてPrincipal Investigator
- Principal Investigator
  
  中島俊樹
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Osaka University

[Journal Article] Explicit forms of cluster variables on double Bruhat cells G^{u,e} of type C2016
- Author(s)
  Y.Kanakubo, T.Nakashima
- Journal Title
  
  Tokyo Journal of Mathematics
  
  Volume : 39 Pages : 643-678
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04794
[Journal Article] Explicit forms of cluster variables on double Bruhat cells $G^{u,e}$ of type C2016
- Author(s)
  Y.Kanakubo and T.Nakashima
- Journal Title
  
  Tokyo J.Math.
  
  Volume : 39
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540026
[Journal Article] Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A2015
- Author(s)
  Toshiki Nakashima(with Y.Kanakubo ）
- Journal Title
  
  SIGMA
  
  Volume : 11 Pages : 033-065
- DOI
  10.3842/sigma.2015.033
- Open Access / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04794
[Journal Article] Cluster Variables on Certain Double Bruhat Cells of Type $(u,e)$ and Monomial Realizations of Crystal Bases of Type A2015
- Author(s)
  Y.Kanakubo and T.Nakashima
- Journal Title
  
  SIGMA(Symmetry Integrability Geom. Methods Appl.)
  
  Volume : 11
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540026
[Journal Article] Decorated Geometric Crystals and Polyhedral Realizations of type D_n2014
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Contemporary Mathematics
  
  Volume : ６２３ Pages : 227-242
- DOI
  10.1090/conm/623/12466
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-22540031, KAKENHI-PROJECT-23540026
[Journal Article] Decorations on geometric crystals and monomial realizations of crystal bases for classical groups2014
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Journal of Algebra
  
  Volume : ３９９ Pages : 712-769
- DOI
  10.1016/j.jalgebra.2013.09.052
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-22540031, KAKENHI-PROJECT-23540026
[Journal Article] Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases2013
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Contemporary Mathematics
  
  Volume : 602 Pages : 143-163
- DOI
  10.1090/conm/602/12025
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540026
[Journal Article] A_n^(1)-Geometric Crystal corresponding to Dynkin index i=2 and its ultra-discretization2013
- Author(s)
  K. Misra and T.Nakashima
- Journal Title
  
  Springer Proceedings in Mathematics & Statistics
  
  Volume : 40 Pages : 297-318
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases2013
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Contemporary Mathematics
  
  Volume : 602 Pages : 143-163
- DOI
  10.1007/978-1-4471-4863-0_12
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] A_n^(1)-Geometric Crystal corresponding to Dynkin index i=2 and its ultra-discretization2013
- Author(s)
  Toshiki Nakashima (with Kailash C. MIsra)
- Journal Title
  
  Springer Proceedings in Mathematics & Statistics
  
  Volume : 40 Pages : 297-318
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540026
[Journal Article] RSK-type correspondence of pictures and Littlewood-Richardson crystals2013
- Author(s)
  Toshiki Nakashima and Miki Shimojo
- Journal Title
  
  Tokyo Journal of Mathematics
  
  Volume : 36 Pages : 113-130
- DOI
  10.3836/tjm/1374497514
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031, KAKENHI-PROJECT-23540026
[Journal Article] Ultra-discretization of the D^(3)_4-Geometric Crystals to the G^(1)_2-Perfect Crystals2012
- Author(s)
  M.Igarashi, Kailash C.Misra and T.Nakashima
- Journal Title
  
  Pacific Journal of Mathematics
  
  Volume : 255 Pages : 117-152
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Geometric Crystals on Flag varieties and Unipotent Subgroups of Classical Groups2011
- Author(s)
  M.Igarashi, T.Nakashima
- Journal Title
  
  Journal of Geometry and Physics
  
  Volume : 61 Pages : 2267-2284
- DOI
  10.1016/j.geomphys.2011.07.001
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031, KAKENHI-PROJECT-23540026
[Journal Article] Pictures and Littlewood-Richardson Crystals2011
- Author(s)
  T.Nakashima, M.Shimojo
- Journal Title
  
  Tokyo Jouranl of Mathematics
  
  Volume : 34 Pages : 493-506
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Admissible Pictures and Littlewood-Richardson Crystals2011
- Author(s)
  T.Nakashima, M.Shimojo
- Journal Title
  
  Communications in Algebra
  
  Volume : 39 Pages : 3849-3865
- DOI
  10.1080/00927872.2010.512590
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031, KAKENHI-PROJECT-23540026
[Journal Article] Pictures and Littlewood-Richardson Crystals2011
- Author(s)
  T.Nakashima and M. Shimojo
- Journal Title
  
  Tokyo Jouranl of Mathematics
  
  Volume : 34 Pages : 493-506
- DOI
  10.3836/tjm/1327931398
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540026
[Journal Article] Affine Geometric Crystal of type D^{(3)}_42010
- Author(s)
  中島俊樹(M.Igarashi)
- Journal Title
  
  Contemporary Mathematics 506
  
  Pages : 215-226
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystal of type D^{(3)}_4.2010
- Author(s)
  中島俊樹(M. Igarashi)
- Journal Title
  
  Contemporary Mathematics 506
  
  Pages : 215-226
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystal of type D^{(3)}_42010
- Author(s)
  M.Igarashi, T.Nakashima
- Journal Title
  
  Contemporary Mathematics
  
  Volume : 506 Pages : 215-226
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Epsilon Systems on Geometric Crystals of type A_n2010
- Author(s)
  T.Nakashima
- Journal Title
  
  Symmetry, Integrability and Geometry : Methods and Applications(SIGMA)
  
  Volume : 6 Pages : 023-14
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Tropical R maps and affine geometric crystals, Represent.2010
- Author(s)
  M.Kashiwara, T.Nakashima, M.Okado
- Journal Title
  
  Theory 14
  
  Pages : 446-509
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540016
[Journal Article] Tropical R maps and affine geometric crystals2010
- Author(s)
  Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
- Journal Title
  
  Represent.Theory
  
  Volume : 14 Pages : 446-509
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340005
[Journal Article] Tropical R maps and Affine Geometric Crystals2010
- Author(s)
  M.Kashiwara, T.Nakashima, M.Okado
- Journal Title
  
  Representation Theory
  
  Volume : 14 Pages : 446-509
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Ultra-discretization of the G^{(1)}_2-Geometric Crystals to the D^{(3)}_4-Perfect Crystals2010
- Author(s)
  M.Igarashi, T.Nakashima
- Journal Title
  
  Progress in Mathematics
  
  Volume : 284 Pages : 273-296
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540031
[Journal Article] Universal tropical R map of sl(2)and prehomogeneous geometric crystals2009
- Author(s)
  T.Nakashima
- Journal Title
  
  RIMS Kokyuroku Bessatu B11
  
  Pages : 101-116
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540024
[Journal Article] Universal tropical R map of sl(2)and prehomogeneous geometric crystals2009
- Author(s)
  中島俊樹
- Journal Title
  
  RIMS Kokyuroku Bessatsu B11
  
  Pages : 101-116
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Universal tropical R map of sl (2) and prehomogeneous geometric crystals2009
- Author(s)
  中島俊樹
- Journal Title
  
  RIMS Kokyuroku Bessatsu B11
  
  Pages : 101-116
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Universal tropical R map of sl(2) and prehomogeneous geometric crystals.2009
- Author(s)
  中島俊樹
- Journal Title
  
  RIMS Kokyuroku Bessatsu B11
  
  Pages : 101-116
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystals and Limit of Perfect Crystals2008
- Author(s)
  中島俊樹(with M. Kashiwara M. Okado)
- Journal Title
  
  Transactions in American Mathematical Society 30
  
  Pages : 3645-3687
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystals and Limit of Perfect Crystals.2008
- Author(s)
  中島俊樹, (M. Kashiwara, M. Okado)
- Journal Title
  
  Transactions in American Mathematical Society 30
  
  Pages : 3645-3687
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine geometric crystals and limit of perfect crystals2008
- Author(s)
  Kashiwara Masaki ; Nakashima Toshiki ; Okado Masato
- Journal Title
  
  Trans. Amer. Math. Soc 360, no.7
  
  Pages : 3645-3686
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340007
[Journal Article] Affine Geometric Crystals and Limitof Perfect Crystals2008
- Author(s)
  中島俊樹(M.Kashiwara M.Okado)
- Journal Title
  
  Transactions in American Mathematical Society 30
  
  Pages : 3645-3687
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystals and Limit of Perfect Crystals2008
- Author(s)
  中島俊樹
- Journal Title
  
  Transactions of American Mathematical Society 360
  
  Pages : 3645-3686
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine geometric crystals and limit of perfect crystals2008
- Author(s)
  M. Kashiwara, Toshiki Nakashima, Masato Okado
- Journal Title
  
  Trans. Amer. Math. Soc. 360,no.7
  
  Pages : 3645-3686
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340007
[Journal Article] Affine Geometric crystal of type G ^(1)_2 ,2007
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Contemporary Mathematics vol. 442
  
  Pages : 179-192
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540047
[Journal Article] Affine geometric crystal of type G^<(1)>22007
- Author(s)
  T. Nakashima
- Journal Title
  
  Contemporary Mathematics 442
  
  Pages : 179-192
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540047
[Journal Article] Affine Geometric Crystal of type G^{(1)}_2.2007
- Author(s)
  中島俊樹
- Journal Title
  
  Contemporary Mathematics 442
  
  Pages : 179-192
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine Geometric Crystal of type G^{(1)}_22007
- Author(s)
  中島俊樹
- Journal Title
  
  Contemporary Mathematics 442
  
  Pages : 179-192
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Affine geometric crystal of type G^(1)_22007
- Author(s)
  T. Nakashima
- Journal Title
  
  Contemporary Mathematics 442
  
  Pages : 157-171
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340007
[Journal Article] Affine Geometric Crystal of type G^{(1)}_22007
- Author(s)
  中島俊樹
- Journal Title
  
  Contemporary Mathematics 442
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540050
[Journal Article] Geometric crystals and affine crystals2006
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Contemporary Mathematics 413
  
  Pages : 157-171
- Data Source
  KAKENHI-PROJECT-18540047
[Journal Article] Evaluation representations and quantum affine algebras at roots of unity2006
- Author(s)
  Y.Abe and T.Nakashima
- Journal Title
  
  Journal of Mathematical Physics 47
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals and affine crystals2006
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Contemporary Mathematics 413
  
  Pages : 157-171
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals and affine crystals2006
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Contemporary Mathematics vol. 413
  
  Pages : 157-171
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540047
[Journal Article] Evaluation representations and quantum affine algebras at roots of unity2006
- Author(s)
  Y.Abe, T.Nakashima
- Journal Title
  
  Journal of Mathematical Physics 47
  
  Pages : 1-28
- Data Source
  KAKENHI-PROJECT-18340007
[Journal Article] Geometric crystals and affine crystals2006
- Author(s)
  T.Nakashima
- Journal Title
  
  Contemp. Math. 413
- Data Source
  KAKENHI-PROJECT-18340007
[Journal Article] Evaluation representations and quantum affine algebras at roots of unity (with Y. Abe)2006
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Journal of Mathematical Physics 47,8
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Nilpotent representations of Classical quantum groups at roots of unity2005
- Author(s)
  Nakashima, Toshiki, Abe, Yuuki
- Journal Title
  
  Journal of Mathematical Physics 46,11
  
  Pages : 113505-113505
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals on Schubert varieties2005
- Author(s)
  T.Nakashima
- Journal Title
  
  J. Geometry and Physics 53
  
  Pages : 197-225
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540042
[Journal Article] Geometric Crystals on Schubert Varieties2005
- Author(s)
  T., Nakashima
- Journal Title
  
  Journal of Geometry and Physics 53
  
  Pages : 197-225
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Polyhedral realizations of crystal bases for modified quantum algebras of type $A$2005
- Author(s)
  Nakashima, Toshiki, Hoshino, Ayumu
- Journal Title
  
  Communications in Algebra 32,7
  
  Pages : 2167-2191
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals on schubert varieties2005
- Author(s)
  T.Nakashima
- Journal Title
  
  Journal of Geometry and Physics 53
  
  Pages : 197-225
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals on Schubert varieties2005
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Journal of Geometry and Physics 53,2
  
  Pages : 198-225
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals on Schubert varieties2005
- Author(s)
  T.Nakashima
- Journal Title
  
  J.Geometry and Physics 53
  
  Pages : 197-225
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540042
[Journal Article] Geometric Crystals on Schubert Varieties2005
- Author(s)
  T.Nakashima
- Journal Title
  
  Journal of Geometry and Physics 53
  
  Pages : 197-225
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Geometric crystals on Schubert varieties2005
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Journal of Geometry and Physics 53
  
  Pages : 197-225
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440006
[Journal Article] Geometric crystals on unipotent groups and generalized Young tableaux2005
- Author(s)
  Nakashima, Toshiki
- Journal Title
  
  Journal of Algebra 289,1
  
  Pages : 65-88
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Extremal projectors of q-boson algebras2004
- Author(s)
  Toshiki Nakashima
- Journal Title
  
  Commun.Math.Phys. 244
  
  Pages : 285-296
- Data Source
  KAKENHI-PROJECT-13440006
[Journal Article] Extremal projectors of q-boson algebras2004
- Author(s)
  T.Nakashima
- Journal Title
  
  Communications in Mathematical Physics 244
  
  Pages : 285-296
- Data Source
  KAKENHI-PROJECT-16540039
[Journal Article] Extremal profectors of q-boson algebras2004
- Author(s)
  T.Nakashima
- Journal Title
  
  Comm. in Math. Physics 244
  
  Pages : 285-296
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540042
[Journal Article] Extremal projectors of q-boson algebras2004
- Author(s)
  T.Nakashima
- Journal Title
  
  Comm.in Math.Physics 244
  
  Pages : 285-296
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540042
[Journal Article] On certain maximal cyclic modules for the quantized special linear algebra at a root of unity2003
- Author(s)
  Masaharu Kaneda, Toshiki Nakashima
- Journal Title
  
  Pacific Journal of Mathmatics 211
  
  Pages : 273-282
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440006
[Journal Article] Polyhedral realizations of crystal bases for modified quantum algebras of type A
- Author(s)
  T.Nakashima, A.Hoshino
- Journal Title
  
  Communications in Algebra (to appear)(発表予定)
- Data Source
  KAKENHI-PROJECT-16540039
[Presentation] Product Structure on Monomial Realizations of Type A fundamental crystals2018
- Author(s)
  T. Nakashima
- Organizer
  Seminaire de Theorie des Groupes, Universit\'e de Picardie
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Geometric Crystals on Cluster Varieties2018
- Author(s)
  T.Nakashima
- Organizer
  S'eminaire d'Algebre, Universite Pierre et Marie Curie,
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Geometric crystals and cluster varieties2017
- Author(s)
  T. Nakashima
- Organizer
  Seminaire d'algebre et de g'eom'etrie, Universite caen Normandie
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Cluster algebras of Finite A Type and Demazure Crystals2017
- Author(s)
  T.Nakashima
- Organizer
  Seminaire Groupes, Representations et Geometrie, Universite Diderot
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] クラスター代数と結晶基底2016
- Author(s)
  中島　俊樹
- Organizer
  研究集会「Tokyo Journal of Mathematics 筱田記念号刊行に寄せて」
- Place of Presentation
  上智大学(東京)
- Year and Date
  2016-03-20
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Affine Geometric Crystal of A^(1)n and Limit of Kirillov-Reshetikhin Perfect Crystals2016
- Author(s)
  中島　俊樹
- Organizer
  日本数学会2016年度秋季分科会
- Place of Presentation
  関西大学(大阪府、吹田市)
- Year and Date
  2016-09-15
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Demazure Crystals and Cluster Algebras2016
- Author(s)
  中島　俊樹
- Organizer
  Algebra Seminar
- Place of Presentation
  North Carolina State University, USA
- Year and Date
  2016-08-12
- Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Affine Geometric Crystals and Limit of KR Perfect Crystals of $A^{(1)}_n$2015
- Author(s)
  T. Nakashima
- Organizer
  8th South Eastern Lie Theory Workshop on Algebraic and Combinatiroal Representaion Theory
- Place of Presentation
  North Carolina State University (USA)
- Year and Date
  2015-10-09
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Affine Geometric Crystals and limit of KR perfect crystals of type A^(1)_n2015
- Author(s)
  中島　俊樹
- Organizer
  South eastern Lie Theory workshop on Algebraic and Combinatorial Representation Theory
- Place of Presentation
  North Carolina State University,(USA)
- Year and Date
  2015-10-09
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15K04794
[Presentation] Polyhedral Realizations of Crystal Bases2015
- Author(s)
  T. Nakashima
- Organizer
  8th South Eastern Lie Theory Workshop on Algebraic and Combinatiroal Representaion Theory, Discussion Sessions
- Place of Presentation
  North Carolina State University (USA)
- Year and Date
  2015-10-10
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Cluster Variables on Double Bruhat cells and Monomial Realizations of Crystal Bases New Directions in Lie Theory2014
- Author(s)
  Toshiki Nakashima
- Organizer
  Combinatorial Representation Theory
- Place of Presentation
  Centre de recherches mathématiques, Montréal, Canada
- Year and Date
  2014-04-23
- Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases2014
- Author(s)
  中島　俊樹
- Organizer
  New Directions in Lie Theory
- Place of Presentation
  Montreal, Canada
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Upper Cluster Algebras on Double Bruhat Cells and Monomial Realizations of Crystal Bases2014
- Author(s)
  Toshiki Nakashima
- Organizer
  ICM satellite Conference on Representation Theory and Related Topics
- Place of Presentation
  EXCO, Daegu, South Korea
- Year and Date
  2014-08-08
- Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Crystal Bases and Upper Cluster Algebras on Double Bruhat Cells2014
- Author(s)
  Toshiki Nakashima
- Organizer
  Conference on Cluster Algebras and Representation Theory
- Place of Presentation
  KIAS, Seoul, South Korea
- Year and Date
  2014-11-06
- Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Monomial realizations of crystal bases and elementary characters2012
- Author(s)
  Toshiki Nakashima
- Organizer
  The XXIX International Colloquium on Group-Theoretic Methods in Physics
- Place of Presentation
  Chern Institute of Mathematics, Tianjin, China
- Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Elementary characters and monomial realizations of crystal bases2012
- Author(s)
  Toshiki Nakashima
- Organizer
  Algebraic and Combinatorial approaches to representation
- Place of Presentation
  University of California Riverside, USA
- Invited
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Geometric Crystals, Elementary Characters and Monomial Realizations of Crystal Bases2011
- Author(s)
  中島　俊樹
- Organizer
  Symmetries, Integrable Systems and Representations(招待講演)
- Place of Presentation
  Lyon, France
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Generalized Minors and Crystal Bases2011
- Author(s)
  中島　俊樹
- Organizer
  可積分系とその周辺(招待講演)
- Place of Presentation
  大阪大学
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Elementary Characters and Monomial Realizations of Crystal Base2011
- Author(s)
  中島　俊樹
- Organizer
  Infinite Analysis 11 Winter School: Quantum cluster algebras and related topics, Graduate School of Science(招待講演)
- Place of Presentation
  大阪大学
- Data Source
  KAKENHI-PROJECT-23540026
[Presentation] Elementary Characters and Monomial Realizations of Crystal Base2011
- Author(s)
  中島俊樹
- Organizer
  Infinite Analysis 11 Winter School : Quantum cluster algebras and related topics, Graduate School of Science
- Place of Presentation
  大阪大学(招待講演)
- Year and Date
  2011-12-23
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Generalized Minors and Crystal Bases2011
- Author(s)
  中島俊樹
- Organizer
  研究会「可積分系とその周辺」
- Place of Presentation
  大阪大学(招待講演)
- Year and Date
  2011-07-02
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Geometric Crystals, Elementary Characters and Monomial Realizations of Crystal Bases2011
- Author(s)
  中島俊樹
- Organizer
  International conference "Symmetries, Integrable Systems and Representations"
- Place of Presentation
  Lyon, France(招待講演)
- Year and Date
  2011-12-15
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] 幾何結晶と多面体表示I,II2010
- Author(s)
  T.Nakashima
- Organizer
  表現論、組み合わせ論とその周辺
- Place of Presentation
  琉球大学
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Decorated Geometric Crystals, Monomial Realizations and Polyhedral Realizations of Crystal Bases2010
- Author(s)
  T.Nakashima
- Organizer
  GCOE Conference : Algebraic and geometric aspects of discrete integrable systems-integrable systems and cluster algebras
- Place of Presentation
  東京大学
- Year and Date
  2010-12-15
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Geometric and Unipotent Bicrystals and Polyhedral Realization of Crystal bases2010
- Author(s)
  T.Nakashima
- Organizer
  ICM Satellite Conference, Algebraic and Combinatorial Approaches to Representation Theory
- Place of Presentation
  National Institute of Advanced Studies, Bangalore, India
- Year and Date
  2010-08-12
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] RSK type correspondcnce of Pictures and Littlewood-Richardson Crystals2010
- Author(s)
  中島俊樹
- Organizer
  2010年日本数学会秋季代数学分科会、無限可積分系セッション
- Place of Presentation
  名古屋大学
- Year and Date
  2010-09-25
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Epsilon Systems of geometric Crystals.2009
- Author(s)
  中島俊樹
- Organizer
  Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems, (A satellite meeting of the Isaac Newton Institute Programme on Desicrete Integrable Systems)
- Place of Presentation
  The University of Glasgow, United Kingdom.
- Year and Date
  2009-03-31
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Admissible Pictures and Littlewood-Richardson Crystals2009
- Author(s)
  中島俊樹
- Organizer
  International workshop on combinatorial and geometric approach to representation theory
- Place of Presentation
  Seoul National University
- Year and Date
  2009-09-21
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Epsilon Systems of geometric Crystals", Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems2009
- Author(s)
  中島俊樹
- Organizer
  A satellite meeting of the Isaac Newton Institute Programme on Desicrete Integrable Systems
- Place of Presentation
  The University of Glasgow, United Kingdom
- Year and Date
  2009-03-31
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Admissible Pictures and Littlewood-Richardson Crystals2009
- Author(s)
  中島俊樹
- Organizer
  International Workshop on Combinatorial and Geometric approach to Representation Theory
- Place of Presentation
  Seoul National University, Korea
- Year and Date
  2009-09-21
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems2009
- Author(s)
  中島俊樹
- Organizer
  Epsilon Systems of geometric Crystals
- Place of Presentation
  Glasgow, United Kingdam
- Year and Date
  2009-03-31
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Affine Tropical R and Prehomogeneous Geometric Crystals.2008
- Author(s)
  中島俊樹
- Organizer
  Quantum Affine Lie Algebras, Extended Affine Lie Algebras, and Applications
- Place of Presentation
  Banff International Research Stations
- Year and Date
  2008-03-05
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Geometric Crystals on flag varieties andmaximal unipotent subgroups2008
- Author(s)
  中島俊樹
- Organizer
  Workshop, 'Crystals and Tropical Combinatorics'
- Place of Presentation
  Kansai Seminar House, 京都
- Year and Date
  2008-08-30
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Geometric Crystals on flag varieties and unipotent radicals2008
- Author(s)
  Toshiki Nakashima
- Organizer
  2008 年度日本数学会総会
- Place of Presentation
  東京工業大学
- Year and Date
  2008-09-26
- Data Source
  KAKENHI-PROJECT-18540047
[Presentation] Affine Tropical R and Prehomogeneous Geometric Crystals2008
- Author(s)
  中島俊樹
- Organizer
  Quantum Affine Lie Algebras, Extended Affine Lie Algebras, and Applications
- Place of Presentation
  Banff International Research Stations, Canada
- Year and Date
  2008-03-05
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Affine Tropical R and Prehomogeneous Geometric Crystals2008
- Author(s)
  中島俊樹
- Organizer
  Quantum Affine Lie Algebras, Extended Affine Lie Algebras, and Applications
- Place of Presentation
  Banff Internationl Research Station,Canada
- Year and Date
  2008-03-05
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Geometric crystals on flag varieties and maximalunipotent radicals2008
- Author(s)
  中島俊樹
- Organizer
  日本数学会
- Place of Presentation
  東京工業大学
- Year and Date
  2008-09-26
- Data Source
  KAKENHI-PROJECT-18540047
[Presentation] Uniqueness of tropical R2007
- Author(s)
  中島俊樹
- Organizer
  組合せ論的表現論の拡がり
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2007-10-25
- Data Source
  KAKENHI-PROJECT-19540050
[Presentation] Affine Geometric Crystals and Tropical R2005
- Author(s)
  T., Nakashima
- Organizer
  Lie Algebras, Vertex Operator Algebras and Their Applications
- Place of Presentation
  Norht Carolina State University, USA
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540039
[Presentation] Affine Geometric Crystals and Tropical R2005
- Author(s)
  中島俊樹
- Organizer
  Lie Algebras, Vertex Operator Algebras and Their Applications
- Place of Presentation
  North Carolina State Univ USA
- Year and Date
  2005-05-17
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540039
[Presentation] Crystal Bases and Upper Cluster Algebras on Double Bruhat Cells
- Author(s)
  Nakashima, Toshiki
- Organizer
  Conference on　Cluster Algebras and Representation Theory,　CMC Thematic Program on Cluster Algebras in Mathematics and Physics
- Place of Presentation
  Seoul, Korea
- Year and Date
  2014-11-04 – 2014-11-07
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Cluster Variables on Double Bruhat cells and Monomial Realizations of Crystal Bases
- Author(s)
  Nakashima, Toshiki
- Organizer
  New Directions in Lie Theory, Combinatorial Representation Theory
- Place of Presentation
  Montreal, Canada
- Year and Date
  2014-04-19 – 2014-04-27
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Elementary characters and monomial realizations of crystal bases
- Author(s)
  中島　俊樹
- Organizer
  Algebraic and Combinatorial approaches to representation
- Place of Presentation
  University of California Riverside, USA
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Upper Cluster Algebras on Double Bruhat Cells and Monomial Realizations of Crystal Bases
- Author(s)
  Nakashima, Toshiki
- Organizer
  ICM satellite Conference on Representation Theory and Related Topics
- Place of Presentation
  Daegu, Korea
- Year and Date
  2014-08-05 – 2014-08-10
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Monomial realizations of crystal bases and elementary characters
- Author(s)
  中島　俊樹
- Organizer
  The XXIX International Colloquium on Group-Theoretic Methods in Physics
- Place of Presentation
  Nankai University, China
- Invited
- Data Source
  KAKENHI-PROJECT-22540031
[Presentation] Decorated Geometric Crystals and Monomial Realizations of Crystals
- Author(s)
  中島　俊樹
- Organizer
  American Mathematical Society Fall SoutheasternSection Meeting,Special Session on Geometric andAlgebraic Aspects of Representation Theory
- Place of Presentation
  Tulane University, New Orleans, USA
- Invited
- Data Source
  KAKENHI-PROJECT-22540031

1. GOMI Yasushi (50276515)

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NAKASHIMA Toshiki 中島 俊樹

中島 俊樹 ナカシマ トシキ

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クラスター代数と結晶基底の表現論的研究Principal InvestigatorOngoing

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Construction of tropical R maps on geometric crystals and its applications to crystal basesPrincipal Investigator

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Construction of affine geometric crystals and Representation theory of crystal basesPrincipal Investigator

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Piecewise Linear Representation Theory of Quantum Groups and Geometric CrystalsPrincipal Investigator

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Combinatorial Representation Theory of Quantum GroupsPrincipal Investigator

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NAKASHIMA Toshiki 中島俊樹

中島俊樹ナカシマトシキ