Edit Profile Nakashima, Toshiki Compute Distance To: Compute 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 all top 5 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. all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0808.17005Kashiwara, Masaki; Nakashima, Toshiki 202 1994 Affine crystals and vertex models. Zbl 0925.17005Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 147 1992 Perfect crystals of quantum affine Lie algebras. Zbl 0774.17017Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 103 1992 Polyhedral realizations of crystal bases for quantized Kac-Moody algebras. Zbl 0897.17014Nakashima, Toshiki; Zelevinsky, Andrei 56 1997 Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Zbl 0795.17016Nakashima, Toshiki 38 1993 Polyhedral realizations of crystal bases for integrable highest weight modules. Zbl 0967.17011Nakashima, Toshiki 36 1999 Affine geometric crystals and limit of perfect crystals. Zbl 1219.17010Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato 15 2008 Geometric crystals on Schubert varieties. Zbl 1156.17304Nakashima, Toshiki 12 2005 Tropical \(R\) maps and affine geometric crystals. Zbl 1220.17006Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato 9 2010 Affine geometric crystal of \(A_n^{(1)}\) and limit of Kirillov-Reshetikhin perfect crystals. Zbl 1433.17018Misra, Kailash C.; Nakashima, Toshiki 6 2018 Polytopes for crystallized Demazure modules and extremal vectors. Zbl 0991.17018Nakashima, Toshiki 6 2002 Polyhedral realizations of crystal bases and braid-type isomorphisms. Zbl 0951.17007Nakashima, Toshiki 6 1999 Crystallized structure for level \(0\) part of modified quantum affine algebra \(\widetilde U_ q(\widehat{sl_ 2})\). Zbl 0888.17006Nakashima, Toshiki 6 1997 Cluster variables on certain double Bruhat cells of type \((u,e)\) and monomial realizations of crystal bases of type A. Zbl 1329.13039Kanakubo, Yuki; Nakashima, Toshiki 5 2015 Decorations on geometric crystals and monomial realizations of crystal bases for classical groups. Zbl 1370.17022Nakashima, Toshiki 5 2014 Vertex models and crystals. Zbl 0776.17008Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 5 1992 Decorated geometric crystals, polyhedral and monomial realizations of crystal bases. Zbl 1370.17021Nakashima, Toshiki 4 2013 Geometric crystals on unipotent groups and generalized Young tableaux. Zbl 1161.17319Nakashima, Toshiki 4 2005 Polyhedral realizations of crystal bases for modified quantum algebras of type \(A^\#\). Zbl 1084.17007Hoshino, Ayumu; Nakashima, Toshiki 4 2005 Extremal projectors of \(q\)-boson algebras. Zbl 1075.17009Nakashima, Toshiki 4 2004 \(A^{(1)}_n\)-geometric crystal corresponding to Dynkin index \(i=2\) and its ultra-discretization. Zbl 1287.17034Misra, Kailash C.; Nakashima, Toshiki 3 2013 Affine geometric crystal of type \(G_2^{(1)}\). Zbl 1142.17010Nakashima, Toshiki 3 2007 Irreducible modules of finite dimensional quantum algebras of type \(A\) at roots of unity. Zbl 1059.17010Nakashima, Toshiki 3 2002 Crystallized Peter-Weyl type decomposition for level 0 part of modified quantum algebra \(\tilde U_ q(\widehat{\mathfrak{sl}_ 2})_ 0\). Zbl 0872.17011Nakashima, Toshiki 3 1997 Quantum \(R\)-matrix and intertwiners for the Kashiwara algebra. Zbl 0806.17011Nakashima, Toshiki 3 1994 Ultra-discretization of the \(D_4^{(3)}\)-geometric crystal to the \(G_2^{(1)}\)-perfect crystals. Zbl 1248.17010Igarashi, Mana; Misra, Kailash C.; Nakashima, Toshiki 2 2012 Admissible pictures and Littlewood-Richardson crystals. Zbl 1235.05148Nakashima, Toshiki; Shimojo, Miki 2 2011 Ultra-discretization of the \(G^{(1)}_2\)-geometric crystals to the \(D^{(3)}_4\)-perfect crystals. Zbl 1259.17016Nakashima, Toshiki 2 2010 Cluster variables on double Bruhat cells \(G^{u,e}\) of classical groups and monomial realizations of Demazure crystals. Zbl 1439.13055Kanakubo, Yuki; Nakashima, Toshiki 1 2018 Explicit forms of cluster variables on double Bruhat cells \(G^{u,e}\) of type C. Zbl 1437.13036Kanakubo, Yuki; Nakashima, Toshiki 1 2017 Decorated geometric crystals and polyhedral realizations of type \(D_n\). Zbl 1357.17018Nakashima, Toshiki 1 2014 Pictures and Littlewood-Richardson crystals. Zbl 1238.05279Nakashima, Toshiki; Shimojo, Miki 1 2011 Affine geometric crystal of type \(D_4^{(3)}\). Zbl 1276.17009Igarashi, Mana; Nakashima, Toshiki 1 2010 Epsilon systems on geometric crystals of type \(A_n\). Zbl 1204.17011Nakashima, Toshiki 1 2010 Universal tropical \(R\) map of \(\mathfrak{sl}_2\) and prehomogeneous geometric crystals. Zbl 1220.17007Nakashima, Toshiki 1 2009 Nilpotent representations of classical quantum groups at roots of unity. Zbl 1111.17006Abe, Yuuki; Nakashima, Toshiki 1 2005 On certain maximal cyclic modules for the quantized special linear algebra at a root of unity. Zbl 1107.17009Kaneda, Masaharu; Nakashima, Toshiki 1 2003 A basis of symmetric tensor representations for the quantum analogue of the Lie algebras \(B_ n, C_ n\) and \(D_ n\). Zbl 0744.17017Nakashima, Toshiki 1 1990 Affine geometric crystal of \(A_n^{(1)}\) and limit of Kirillov-Reshetikhin perfect crystals. Zbl 1433.17018Misra, Kailash C.; Nakashima, Toshiki 6 2018 Cluster variables on double Bruhat cells \(G^{u,e}\) of classical groups and monomial realizations of Demazure crystals. Zbl 1439.13055Kanakubo, Yuki; Nakashima, Toshiki 1 2018 Explicit forms of cluster variables on double Bruhat cells \(G^{u,e}\) of type C. Zbl 1437.13036Kanakubo, Yuki; Nakashima, Toshiki 1 2017 Cluster variables on certain double Bruhat cells of type \((u,e)\) and monomial realizations of crystal bases of type A. Zbl 1329.13039Kanakubo, Yuki; Nakashima, Toshiki 5 2015 Decorations on geometric crystals and monomial realizations of crystal bases for classical groups. Zbl 1370.17022Nakashima, Toshiki 5 2014 Decorated geometric crystals and polyhedral realizations of type \(D_n\). Zbl 1357.17018Nakashima, Toshiki 1 2014 Decorated geometric crystals, polyhedral and monomial realizations of crystal bases. Zbl 1370.17021Nakashima, Toshiki 4 2013 \(A^{(1)}_n\)-geometric crystal corresponding to Dynkin index \(i=2\) and its ultra-discretization. Zbl 1287.17034Misra, Kailash C.; Nakashima, Toshiki 3 2013 Ultra-discretization of the \(D_4^{(3)}\)-geometric crystal to the \(G_2^{(1)}\)-perfect crystals. Zbl 1248.17010Igarashi, Mana; Misra, Kailash C.; Nakashima, Toshiki 2 2012 Admissible pictures and Littlewood-Richardson crystals. Zbl 1235.05148Nakashima, Toshiki; Shimojo, Miki 2 2011 Pictures and Littlewood-Richardson crystals. Zbl 1238.05279Nakashima, Toshiki; Shimojo, Miki 1 2011 Tropical \(R\) maps and affine geometric crystals. Zbl 1220.17006Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato 9 2010 Ultra-discretization of the \(G^{(1)}_2\)-geometric crystals to the \(D^{(3)}_4\)-perfect crystals. Zbl 1259.17016Nakashima, Toshiki 2 2010 Affine geometric crystal of type \(D_4^{(3)}\). Zbl 1276.17009Igarashi, Mana; Nakashima, Toshiki 1 2010 Epsilon systems on geometric crystals of type \(A_n\). Zbl 1204.17011Nakashima, Toshiki 1 2010 Universal tropical \(R\) map of \(\mathfrak{sl}_2\) and prehomogeneous geometric crystals. Zbl 1220.17007Nakashima, Toshiki 1 2009 Affine geometric crystals and limit of perfect crystals. Zbl 1219.17010Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato 15 2008 Affine geometric crystal of type \(G_2^{(1)}\). Zbl 1142.17010Nakashima, Toshiki 3 2007 Geometric crystals on Schubert varieties. Zbl 1156.17304Nakashima, Toshiki 12 2005 Geometric crystals on unipotent groups and generalized Young tableaux. Zbl 1161.17319Nakashima, Toshiki 4 2005 Polyhedral realizations of crystal bases for modified quantum algebras of type \(A^\#\). Zbl 1084.17007Hoshino, Ayumu; Nakashima, Toshiki 4 2005 Nilpotent representations of classical quantum groups at roots of unity. Zbl 1111.17006Abe, Yuuki; Nakashima, Toshiki 1 2005 Extremal projectors of \(q\)-boson algebras. Zbl 1075.17009Nakashima, Toshiki 4 2004 On certain maximal cyclic modules for the quantized special linear algebra at a root of unity. Zbl 1107.17009Kaneda, Masaharu; Nakashima, Toshiki 1 2003 Polytopes for crystallized Demazure modules and extremal vectors. Zbl 0991.17018Nakashima, Toshiki 6 2002 Irreducible modules of finite dimensional quantum algebras of type \(A\) at roots of unity. Zbl 1059.17010Nakashima, Toshiki 3 2002 Polyhedral realizations of crystal bases for integrable highest weight modules. Zbl 0967.17011Nakashima, Toshiki 36 1999 Polyhedral realizations of crystal bases and braid-type isomorphisms. Zbl 0951.17007Nakashima, Toshiki 6 1999 Polyhedral realizations of crystal bases for quantized Kac-Moody algebras. Zbl 0897.17014Nakashima, Toshiki; Zelevinsky, Andrei 56 1997 Crystallized structure for level \(0\) part of modified quantum affine algebra \(\widetilde U_ q(\widehat{sl_ 2})\). Zbl 0888.17006Nakashima, Toshiki 6 1997 Crystallized Peter-Weyl type decomposition for level 0 part of modified quantum algebra \(\tilde U_ q(\widehat{\mathfrak{sl}_ 2})_ 0\). Zbl 0872.17011Nakashima, Toshiki 3 1997 Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras. Zbl 0808.17005Kashiwara, Masaki; Nakashima, Toshiki 202 1994 Quantum \(R\)-matrix and intertwiners for the Kashiwara algebra. Zbl 0806.17011Nakashima, Toshiki 3 1994 Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Zbl 0795.17016Nakashima, Toshiki 38 1993 Affine crystals and vertex models. Zbl 0925.17005Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 147 1992 Perfect crystals of quantum affine Lie algebras. Zbl 0774.17017Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 103 1992 Vertex models and crystals. Zbl 0776.17008Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi 5 1992 A basis of symmetric tensor representations for the quantum analogue of the Lie algebras \(B_ n, C_ n\) and \(D_ n\). Zbl 0744.17017Nakashima, Toshiki 1 1990 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year