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## Nakashima, Toshiki

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 Author ID: nakashima.toshiki Published as: Nakashima, Toshiki Homepage: http://rscdb.cc.sophia.ac.jp/Profiles/57/0005692/prof_e.html
 Documents Indexed: 48 Publications since 1990, including 1 Book
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#### Co-Authors

 21 single-authored 6 Kanakubo, Yuki 6 Kashiwara, Masaki 6 Misra, Kailash C. 4 Miwa, Tetsuji 3 Igarashi, Mana 3 Kang, Seok-Jin 3 Nakayashiki, Atsushi 3 Shimojo, Miki 2 Abe, Yuuki 2 Okado, Masato 1 Alshuqayr, Manal 1 Hoshino, Ayumu 1 Kaneda, Masaharu 1 Matsuo, Atsushi 1 Saito, Yoshihisa 1 Zelevinskiĭ, Andreĭ V.
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#### Serials

 7 Journal of Algebra 4 Communications in Algebra 4 Tokyo Journal of Mathematics 3 Communications in Mathematical Physics 3 Journal of Mathematical Physics 3 Journal of Geometry and Physics 2 Pacific Journal of Mathematics 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 International Journal of Modern Physics A 1 Advances in Mathematics 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Transactions of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Representation Theory 1 Advanced Studies in Pure Mathematics 1 RIMS Kôkyûroku Bessatsu
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#### Fields

 45 Nonassociative rings and algebras (17-XX) 14 Algebraic geometry (14-XX) 8 Topological groups, Lie groups (22-XX) 8 Quantum theory (81-XX) 6 Group theory and generalizations (20-XX) 5 Commutative algebra (13-XX) 4 Combinatorics (05-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Differential geometry (53-XX)

#### Citations contained in zbMATH

38 Publications have been cited 704 times in 354 Documents Cited by Year
Crystal graphs for representations of the $$q$$-analogue of classical Lie algebras. Zbl 0808.17005
Kashiwara, Masaki; Nakashima, Toshiki
1994
Affine crystals and vertex models. Zbl 0925.17005
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
Perfect crystals of quantum affine Lie algebras. Zbl 0774.17017
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
Polyhedral realizations of crystal bases for quantized Kac-Moody algebras. Zbl 0897.17014
Nakashima, Toshiki; Zelevinsky, Andrei
1997
Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Zbl 0795.17016
Nakashima, Toshiki
1993
Polyhedral realizations of crystal bases for integrable highest weight modules. Zbl 0967.17011
Nakashima, Toshiki
1999
Affine geometric crystals and limit of perfect crystals. Zbl 1219.17010
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
2008
Geometric crystals on Schubert varieties. Zbl 1156.17304
Nakashima, Toshiki
2005
Tropical $$R$$ maps and affine geometric crystals. Zbl 1220.17006
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
2010
Affine geometric crystal of $$A_n^{(1)}$$ and limit of Kirillov-Reshetikhin perfect crystals. Zbl 1433.17018
Misra, Kailash C.; Nakashima, Toshiki
2018
Polytopes for crystallized Demazure modules and extremal vectors. Zbl 0991.17018
Nakashima, Toshiki
2002
Polyhedral realizations of crystal bases and braid-type isomorphisms. Zbl 0951.17007
Nakashima, Toshiki
1999
Crystallized structure for level $$0$$ part of modified quantum affine algebra $$\widetilde U_ q(\widehat{sl_ 2})$$. Zbl 0888.17006
Nakashima, Toshiki
1997
Cluster variables on certain double Bruhat cells of type $$(u,e)$$ and monomial realizations of crystal bases of type A. Zbl 1329.13039
Kanakubo, Yuki; Nakashima, Toshiki
2015
Decorations on geometric crystals and monomial realizations of crystal bases for classical groups. Zbl 1370.17022
Nakashima, Toshiki
2014
Vertex models and crystals. Zbl 0776.17008
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
Decorated geometric crystals, polyhedral and monomial realizations of crystal bases. Zbl 1370.17021
Nakashima, Toshiki
2013
Geometric crystals on unipotent groups and generalized Young tableaux. Zbl 1161.17319
Nakashima, Toshiki
2005
Polyhedral realizations of crystal bases for modified quantum algebras of type $$A^\#$$. Zbl 1084.17007
Hoshino, Ayumu; Nakashima, Toshiki
2005
Extremal projectors of $$q$$-boson algebras. Zbl 1075.17009
Nakashima, Toshiki
2004
$$A^{(1)}_n$$-geometric crystal corresponding to Dynkin index $$i=2$$ and its ultra-discretization. Zbl 1287.17034
Misra, Kailash C.; Nakashima, Toshiki
2013
Affine geometric crystal of type $$G_2^{(1)}$$. Zbl 1142.17010
Nakashima, Toshiki
2007
Irreducible modules of finite dimensional quantum algebras of type $$A$$ at roots of unity. Zbl 1059.17010
Nakashima, Toshiki
2002
Crystallized Peter-Weyl type decomposition for level 0 part of modified quantum algebra $$\tilde U_ q(\widehat{\mathfrak{sl}_ 2})_ 0$$. Zbl 0872.17011
Nakashima, Toshiki
1997
Quantum $$R$$-matrix and intertwiners for the Kashiwara algebra. Zbl 0806.17011
Nakashima, Toshiki
1994
Ultra-discretization of the $$D_4^{(3)}$$-geometric crystal to the $$G_2^{(1)}$$-perfect crystals. Zbl 1248.17010
Igarashi, Mana; Misra, Kailash C.; Nakashima, Toshiki
2012
Admissible pictures and Littlewood-Richardson crystals. Zbl 1235.05148
Nakashima, Toshiki; Shimojo, Miki
2011
Ultra-discretization of the $$G^{(1)}_2$$-geometric crystals to the $$D^{(3)}_4$$-perfect crystals. Zbl 1259.17016
Nakashima, Toshiki
2010
Cluster variables on double Bruhat cells $$G^{u,e}$$ of classical groups and monomial realizations of Demazure crystals. Zbl 1439.13055
Kanakubo, Yuki; Nakashima, Toshiki
2018
Explicit forms of cluster variables on double Bruhat cells $$G^{u,e}$$ of type C. Zbl 1437.13036
Kanakubo, Yuki; Nakashima, Toshiki
2017
Decorated geometric crystals and polyhedral realizations of type $$D_n$$. Zbl 1357.17018
Nakashima, Toshiki
2014
Pictures and Littlewood-Richardson crystals. Zbl 1238.05279
Nakashima, Toshiki; Shimojo, Miki
2011
Affine geometric crystal of type $$D_4^{(3)}$$. Zbl 1276.17009
Igarashi, Mana; Nakashima, Toshiki
2010
Epsilon systems on geometric crystals of type $$A_n$$. Zbl 1204.17011
Nakashima, Toshiki
2010
Universal tropical $$R$$ map of $$\mathfrak{sl}_2$$ and prehomogeneous geometric crystals. Zbl 1220.17007
Nakashima, Toshiki
2009
Nilpotent representations of classical quantum groups at roots of unity. Zbl 1111.17006
Abe, Yuuki; Nakashima, Toshiki
2005
On certain maximal cyclic modules for the quantized special linear algebra at a root of unity. Zbl 1107.17009
Kaneda, Masaharu; Nakashima, Toshiki
2003
A basis of symmetric tensor representations for the quantum analogue of the Lie algebras $$B_ n, C_ n$$ and $$D_ n$$. Zbl 0744.17017
Nakashima, Toshiki
1990
Affine geometric crystal of $$A_n^{(1)}$$ and limit of Kirillov-Reshetikhin perfect crystals. Zbl 1433.17018
Misra, Kailash C.; Nakashima, Toshiki
2018
Cluster variables on double Bruhat cells $$G^{u,e}$$ of classical groups and monomial realizations of Demazure crystals. Zbl 1439.13055
Kanakubo, Yuki; Nakashima, Toshiki
2018
Explicit forms of cluster variables on double Bruhat cells $$G^{u,e}$$ of type C. Zbl 1437.13036
Kanakubo, Yuki; Nakashima, Toshiki
2017
Cluster variables on certain double Bruhat cells of type $$(u,e)$$ and monomial realizations of crystal bases of type A. Zbl 1329.13039
Kanakubo, Yuki; Nakashima, Toshiki
2015
Decorations on geometric crystals and monomial realizations of crystal bases for classical groups. Zbl 1370.17022
Nakashima, Toshiki
2014
Decorated geometric crystals and polyhedral realizations of type $$D_n$$. Zbl 1357.17018
Nakashima, Toshiki
2014
Decorated geometric crystals, polyhedral and monomial realizations of crystal bases. Zbl 1370.17021
Nakashima, Toshiki
2013
$$A^{(1)}_n$$-geometric crystal corresponding to Dynkin index $$i=2$$ and its ultra-discretization. Zbl 1287.17034
Misra, Kailash C.; Nakashima, Toshiki
2013
Ultra-discretization of the $$D_4^{(3)}$$-geometric crystal to the $$G_2^{(1)}$$-perfect crystals. Zbl 1248.17010
Igarashi, Mana; Misra, Kailash C.; Nakashima, Toshiki
2012
Admissible pictures and Littlewood-Richardson crystals. Zbl 1235.05148
Nakashima, Toshiki; Shimojo, Miki
2011
Pictures and Littlewood-Richardson crystals. Zbl 1238.05279
Nakashima, Toshiki; Shimojo, Miki
2011
Tropical $$R$$ maps and affine geometric crystals. Zbl 1220.17006
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
2010
Ultra-discretization of the $$G^{(1)}_2$$-geometric crystals to the $$D^{(3)}_4$$-perfect crystals. Zbl 1259.17016
Nakashima, Toshiki
2010
Affine geometric crystal of type $$D_4^{(3)}$$. Zbl 1276.17009
Igarashi, Mana; Nakashima, Toshiki
2010
Epsilon systems on geometric crystals of type $$A_n$$. Zbl 1204.17011
Nakashima, Toshiki
2010
Universal tropical $$R$$ map of $$\mathfrak{sl}_2$$ and prehomogeneous geometric crystals. Zbl 1220.17007
Nakashima, Toshiki
2009
Affine geometric crystals and limit of perfect crystals. Zbl 1219.17010
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
2008
Affine geometric crystal of type $$G_2^{(1)}$$. Zbl 1142.17010
Nakashima, Toshiki
2007
Geometric crystals on Schubert varieties. Zbl 1156.17304
Nakashima, Toshiki
2005
Geometric crystals on unipotent groups and generalized Young tableaux. Zbl 1161.17319
Nakashima, Toshiki
2005
Polyhedral realizations of crystal bases for modified quantum algebras of type $$A^\#$$. Zbl 1084.17007
Hoshino, Ayumu; Nakashima, Toshiki
2005
Nilpotent representations of classical quantum groups at roots of unity. Zbl 1111.17006
Abe, Yuuki; Nakashima, Toshiki
2005
Extremal projectors of $$q$$-boson algebras. Zbl 1075.17009
Nakashima, Toshiki
2004
On certain maximal cyclic modules for the quantized special linear algebra at a root of unity. Zbl 1107.17009
Kaneda, Masaharu; Nakashima, Toshiki
2003
Polytopes for crystallized Demazure modules and extremal vectors. Zbl 0991.17018
Nakashima, Toshiki
2002
Irreducible modules of finite dimensional quantum algebras of type $$A$$ at roots of unity. Zbl 1059.17010
Nakashima, Toshiki
2002
Polyhedral realizations of crystal bases for integrable highest weight modules. Zbl 0967.17011
Nakashima, Toshiki
1999
Polyhedral realizations of crystal bases and braid-type isomorphisms. Zbl 0951.17007
Nakashima, Toshiki
1999
Polyhedral realizations of crystal bases for quantized Kac-Moody algebras. Zbl 0897.17014
Nakashima, Toshiki; Zelevinsky, Andrei
1997
Crystallized structure for level $$0$$ part of modified quantum affine algebra $$\widetilde U_ q(\widehat{sl_ 2})$$. Zbl 0888.17006
Nakashima, Toshiki
1997
Crystallized Peter-Weyl type decomposition for level 0 part of modified quantum algebra $$\tilde U_ q(\widehat{\mathfrak{sl}_ 2})_ 0$$. Zbl 0872.17011
Nakashima, Toshiki
1997
Crystal graphs for representations of the $$q$$-analogue of classical Lie algebras. Zbl 0808.17005
Kashiwara, Masaki; Nakashima, Toshiki
1994
Quantum $$R$$-matrix and intertwiners for the Kashiwara algebra. Zbl 0806.17011
Nakashima, Toshiki
1994
Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Zbl 0795.17016
Nakashima, Toshiki
1993
Affine crystals and vertex models. Zbl 0925.17005
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
Perfect crystals of quantum affine Lie algebras. Zbl 0774.17017
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
Vertex models and crystals. Zbl 0776.17008
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi
1992
A basis of symmetric tensor representations for the quantum analogue of the Lie algebras $$B_ n, C_ n$$ and $$D_ n$$. Zbl 0744.17017
Nakashima, Toshiki
1990
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#### Cited by 241 Authors

 26 Okado, Masato 25 Kang, Seok-Jin 23 Nakashima, Toshiki 20 Kwon, Jae-Hoon 20 Shin, Dong-Uy 19 Kim, Jeong-Ah 19 Misra, Kailash C. 18 Schilling, Anne 18 Scrimshaw, Travis 16 Kashiwara, Masaki 16 Kuniba, Atsuo 16 Lee, Hyeonmi 11 Lecouvey, Cédric 10 Takagi, Taichiro 9 Kim, Myungho 9 Shimozono, Mark 8 Park, Euiyong 6 Hong, Jin 6 Jung, Ji Hye 6 Koshevoy, Gleb A. 6 Lenart, Cristian 6 Sakamoto, Reiho 6 Salisbury, Ben 5 Donnelly, Robert G. 5 Hoshino, Ayumu 5 Kanakubo, Yuki 5 Lam, Thomas F. 5 Marsh, Robert James 5 Miwa, Tetsuji 5 Nakayashiki, Atsushi 5 Oh, Se-jin 5 Pylyavskyy, Pavlo 4 Assaf, Sami H. 4 Danilov, Vladimir I. 4 Gade, R. M. 4 Grantcharov, Dimitar 4 Hatayama, Goro 4 Jimbo, Michio 4 Jing, Naihuan 4 Kamnitzer, Joel 4 Karzanov, Aleksandr V. 4 Naito, Satoshi 4 Yamada, Yasuhiko 3 Abe, Yuuki 3 Brundan, Jonathan 3 Cain, Alan J. 3 Choi, Seungil 3 Dousse, Jehanne 3 Foda, Omar 3 Fujita, Naoki 3 Gerber, Thomas 3 Inoue, Rei 3 Kus, Deniz 3 Lee, Kyu-Hwan 3 Lubovsky, Arthur 3 Malheiro, António 3 Nakanishi, Tomoki 3 Premat, Alejandra 3 Primc, Mirko 3 Sagaki, Daisuke 3 Shimojo, Miki 3 Sthanumoorthy, Neelacanta 3 Torres, Jacinta 3 Uchiyama, Jun 3 Uma Maheswari, A. 3 Vavilov, Nikolaĭ Aleksandrovich 3 Wilson, Evan A. 2 Aas, Erik 2 Ariki, Susumu 2 Caldero, Philippe 2 Chepuri, Sunita 2 Defosseux, Manon 2 Dołȩga, Maciej 2 Dusel, John M. 2 Feĭgin, Boris L’vovich 2 Fourier, Ghislain 2 Frieden, Gabriel 2 Grinberg, Darij 2 Gunawan, Emily 2 Henriques, André G. 2 Hernandez, David 2 Igarashi, Mana 2 Jang, Il-Seung 2 Joseph, Anthony 2 Kim, Sungsoon 2 Kirillov, Anatol N. 2 Krob, Daniel 2 Leclerc, Bernard 2 Naoi, Katsuyuki 2 Oğuz, Ezgi Kantarcı 2 Pongprasert, Suchada 2 Savage, Alistair 2 Sternberg, Philip 2 Thibon, Jean-Yves 2 Tsuchioka, Shunsuke 2 Vazirani, Monica J. 2 Yamada, Daisuke 1 Agrebaoui, Boujemaa 1 Akasaka, Tatsuya 1 Alshuqayr, Manal ...and 141 more Authors
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#### Cited in 54 Serials

 66 Journal of Algebra 27 Communications in Algebra 24 Journal of Algebraic Combinatorics 19 Journal of Combinatorial Theory. Series A 18 Algebras and Representation Theory 16 Journal of Mathematical Physics 16 Advances in Mathematics 14 Communications in Mathematical Physics 14 Nuclear Physics. B 14 Transactions of the American Mathematical Society 13 Séminaire Lotharingien de Combinatoire 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Duke Mathematical Journal 7 European Journal of Combinatorics 7 Transformation Groups 6 Selecta Mathematica. New Series 5 Proceedings of the American Mathematical Society 5 Representation Theory 4 Letters in Mathematical Physics 4 Journal of Geometry and Physics 4 Journal of Pure and Applied Algebra 4 Mathematische Zeitschrift 4 Tokyo Journal of Mathematics 3 Theoretical and Mathematical Physics 3 Compositio Mathematica 3 International Journal of Algebra and Computation 2 International Journal of Modern Physics A 2 Discrete Mathematics 2 Mathematische Annalen 2 Nagoya Mathematical Journal 2 International Journal of Mathematics 2 Bulletin des Sciences Mathématiques 2 Algebraic Combinatorics 1 Reviews in Mathematical Physics 1 Proceedings of the Japan Academy. Series A 1 Rendiconti del Seminario Matematico della Università di Padova 1 Advances in Applied Mathematics 1 Journal of Theoretical Probability 1 Journal of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Algebra Colloquium 1 St. Petersburg Mathematical Journal 1 The Electronic Journal of Combinatorics 1 Annals of Combinatorics 1 LMS Journal of Computation and Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Annales Henri Poincaré 1 Central European Journal of Mathematics 1 Journal of Algebra and its Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Frontiers of Mathematics in China 1 Science China. Mathematics 1 ISRN Combinatorics 1 Algebra
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#### Cited in 25 Fields

 281 Nonassociative rings and algebras (17-XX) 162 Combinatorics (05-XX) 74 Quantum theory (81-XX) 49 Group theory and generalizations (20-XX) 40 Statistical mechanics, structure of matter (82-XX) 26 Algebraic geometry (14-XX) 19 Topological groups, Lie groups (22-XX) 17 Associative rings and algebras (16-XX) 10 Commutative algebra (13-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Computer science (68-XX) 8 Category theory; homological algebra (18-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Convex and discrete geometry (52-XX) 3 Special functions (33-XX) 3 Probability theory and stochastic processes (60-XX) 2 Partial differential equations (35-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)