Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin; Park, Euiyong Cluster algebra structures on module categories over quantum affine algebras. (English) Zbl 07730902 Proc. Lond. Math. Soc. (3) 124, No. 3, 301-372 (2022). MSC: 81R50 18D15 17B67 13C05 13F60 13D15 16G20 20B05 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Proc. Lond. Math. Soc. (3) 124, No. 3, 301--372 (2022; Zbl 07730902) Full Text: DOI arXiv
Kashiwara, Masaki; Park, Euiyong Categorical crystals for quantum affine algebras. (English) Zbl 1523.17033 J. Reine Angew. Math. 792, 223-267 (2022). MSC: 17B37 05E16 17B10 17B67 18B99 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{E. Park}, J. Reine Angew. Math. 792, 223--267 (2022; Zbl 1523.17033) Full Text: DOI arXiv
Kashiwara, Masaki; Oh, Se-jin Categorical relations between Langlands dual quantum affine algebras: doubly laced types. (English) Zbl 1479.17027 J. Algebr. Comb. 49, No. 4, 401-435 (2019). Reviewer: Chun-Ju Lai (Taipei) MSC: 17B37 16G20 16T30 17B67 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{S.-j. Oh}, J. Algebr. Comb. 49, No. 4, 401--435 (2019; Zbl 1479.17027) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho; Oh, Se-Jin Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. IV. (English) Zbl 1354.81030 Sel. Math., New Ser. 22, No. 4, 1987-2015 (2016). MSC: 17B37 20C08 17B67 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Sel. Math., New Ser. 22, No. 4, 1987--2015 (2016; Zbl 1354.81030) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Tsuchioka, Shunsuke Quiver Hecke superalgebras. (English) Zbl 1360.17018 J. Reine Angew. Math. 711, 1-54 (2016). Reviewer: Jan E. Grabowski (Lancaster) MSC: 17B37 20C08 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., J. Reine Angew. Math. 711, 1--54 (2016; Zbl 1360.17018) Full Text: DOI arXiv
Kahng, Byeong Hoon; Kang, Seok-Jin; Kashiwara, Masaki; Suh, Uhi Rinn Dual perfect bases and dual perfect graphs. (English) Zbl 1383.17008 Mosc. Math. J. 15, No. 2, 319-335 (2015). MSC: 17B37 17B10 20G42 PDFBibTeX XMLCite \textit{B. H. Kahng} et al., Mosc. Math. J. 15, No. 2, 319--335 (2015; Zbl 1383.17008) Full Text: arXiv Link
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho; Oh, Se-Jin Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. III. (English) Zbl 1322.81056 Proc. Lond. Math. Soc. (3) 111, No. 2, 420-444 (2015). MSC: 17B37 20C08 17B67 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Proc. Lond. Math. Soc. (3) 111, No. 2, 420--444 (2015; Zbl 1322.81056) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. II. (English) Zbl 1323.81046 Duke Math. J. 164, No. 8, 1549-1602 (2015). Reviewer: Hu Jun (Beijing) MSC: 17B37 20C08 17B67 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Duke Math. J. 164, No. 8, 1549--1602 (2015; Zbl 1323.81046) Full Text: DOI arXiv Euclid
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho; Oh, Se-Jin Simplicity of heads and socles of tensor products. (English) Zbl 1366.17014 Compos. Math. 151, No. 2, 377-396 (2015). MSC: 17B37 17B67 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Compos. Math. 151, No. 2, 377--396 (2015; Zbl 1366.17014) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Oh, Se-Jin Categorification of highest weight modules over quantum generalized Kac-Moody algebras. (English) Zbl 1290.05158 Mosc. Math. J. 13, No. 2, 315-343 (2013). MSC: 17B37 05E10 17B10 17B67 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Mosc. Math. J. 13, No. 2, 315--343 (2013; Zbl 1290.05158) Full Text: arXiv Link
Kang, Seok-Jin; Kashiwara, Masaki; Oh, Se-jin Supercategorification of quantum Kac-Moody algebras. I, II. (English) Zbl 1304.17012 Adv. Math. 242, 116-162 (2013); 265, 169-240 (2014). Reviewer: Jan E. Grabowski (Lancaster) MSC: 17B37 05E10 16G99 17B67 17C70 81R10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Adv. Math. 242, 116--162 (2013; Zbl 1304.17012) Full Text: DOI DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Park, Euiyong Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data. (English) Zbl 1281.14011 Proc. Lond. Math. Soc. (3) 107, No. 4, 907-931 (2013). Reviewer: Jiuzu Hong (Tel Aviv) MSC: 17B37 14F05 17B67 14F43 81R10 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Proc. Lond. Math. Soc. (3) 107, No. 4, 907--931 (2013; Zbl 1281.14011) Full Text: DOI arXiv
Kashiwara, Masaki Equivariant derived category and representation of real semisimple Lie groups. (English) Zbl 1173.22010 Casadio Tarabusi, Enrico (ed.) et al., Representation theory and complex analysis. Lectures given at the C.I.M.E. summer school, Venice, Italy, June 10–17, 2004. Berlin: Springer (ISBN 978-3-540-76891-3/pbk). Lecture Notes in Mathematics 1931, 137-234 (2008). Reviewer: Pavle Pandžić (Zagreb) MSC: 22E46 14F05 14F10 PDFBibTeX XMLCite \textit{M. Kashiwara}, Lect. Notes Math. 1931, 137--234 (2008; Zbl 1173.22010) Full Text: DOI
Jeong, Kyeonghoon; Kang, Seok-Jin; Kashiwara, Masaki; Shin, Dong-Uy Abstract crystals for quantum generalized Kac-Moody algebras. (English) Zbl 1130.17008 Int. Math. Res. Not. 2007, No. 1, Article ID rnm001, 18 p. (2007). Reviewer: Robert Marsh (Leeds) MSC: 17B37 17B10 17B67 PDFBibTeX XMLCite \textit{K. Jeong} et al., Int. Math. Res. Not. 2007, No. 1, Article ID rnm001, 18 p. (2007; Zbl 1130.17008) Full Text: DOI arXiv
Kashiwara, Masaki Realizations of crystals. (English) Zbl 1066.17006 Kang, Seok-Jin (ed.) et al., Combinatorial and geometric representation theory. An international conference, Seoul, Korea, October 22–26, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3212-3/pbk). Contemp. Math. 325, 133-139 (2003). Reviewer: Sonia Natale (Cordoba) MSC: 17B37 17B10 20G05 PDFBibTeX XMLCite \textit{M. Kashiwara}, Contemp. Math. 325, 133--139 (2003; Zbl 1066.17006) Full Text: arXiv
Kashiwara, Masaki Cochet, Charles (ed.) Crystalline bases of quantum groups. Edited by Charles Cochet. (Bases cristallines des groupes quantiques.) (French) Zbl 1066.17007 Cours Spécialisés (Paris) 9. Paris: Société Mathématique de France (ISBN 2-85629-126-0/pbk). viii, 115 p. (2002). Reviewer: Angela Gammella (Creil) MSC: 17B37 17-02 17B10 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{C. Cochet} (ed.), Bases cristallines des groupes quantiques. Paris: Société Mathématique de France (2002; Zbl 1066.17007)
Barlet, Daniel; Kashiwara, Masaki Duality of D-modules on flag manifolds. (English) Zbl 1018.22012 Int. Math. Res. Not. 2000, No. 23, 1243-1257 (2000). Reviewer: V.Lakshmibai (Boston) MSC: 22E47 32C38 PDFBibTeX XMLCite \textit{D. Barlet} and \textit{M. Kashiwara}, Int. Math. Res. Not. 2000, No. 23, 1243--1257 (2000; Zbl 1018.22012) Full Text: DOI
Kang, Seok-Jin; Kashiwara, Masaki Quantized affine algebras and crystals with core. (English) Zbl 0929.17011 Commun. Math. Phys. 195, No. 3, 725-740 (1998). Reviewer: Xu Xiaoping (Kowloon) MSC: 17B37 17B10 PDFBibTeX XMLCite \textit{S.-J. Kang} and \textit{M. Kashiwara}, Commun. Math. Phys. 195, No. 3, 725--740 (1998; Zbl 0929.17011) Full Text: DOI arXiv
Kashiwara, Masaki; Saito, Yoshihisa Geometric construction of crystal bases. (English) Zbl 0901.17006 Duke Math. J. 89, No. 1, 9-36 (1997). Reviewer: H.H.Andersen (Aarhus) MSC: 17B37 17B10 20G05 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{Y. Saito}, Duke Math. J. 89, No. 1, 9--36 (1997; Zbl 0901.17006) Full Text: DOI arXiv
Kashiwara, Masaki; Tanisaki, Toshiyuki Kazhdan-Lusztig conjecture for affine Lie algebras with negative level. II: Nonintegral case. (English) Zbl 0929.17027 Duke Math. J. 84, No. 3, 771-813 (1996). Reviewer: K.C.Misra (Raleigh) MSC: 17B67 17B10 22E47 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Tanisaki}, Duke Math. J. 84, No. 3, 771--813 (1996; Zbl 0929.17027) Full Text: DOI
Kashiwara, Masaki; Tanisaki, Toshiyuki Kazhdan-Lusztig conjecture for affine Lie algebras with negative level. (English) Zbl 0829.17020 Duke Math. J. 77, No. 1, 21-62 (1995). Reviewer: K.C.Misra (Raleigh) MSC: 17B67 22E47 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Tanisaki}, Duke Math. J. 77, No. 1, 21--62 (1995; Zbl 0829.17020) Full Text: DOI
Kashiwara, M.; Tanisaki, T. The Kazhdan-Lusztig conjecture for Kac-Moody Lie algebras. (Japanese) Zbl 0900.17007 Yamada, Hirofumi (ed.), Noncommutative analysis on homogeneous spaces. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, August 2–5, 1994. Kyoto: Kyoto Univ., Research Institute for Mathematical Sciences, RIMS Kôkyûroku. 895, 44-66 (1995). MSC: 17B67 17B10 22E65 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Tanisaki}, in: Noncommutative analysis on homogeneous spaces. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, August 2--5, 1994. Kyoto: Kyoto Univ., Research Institute for Mathematical Sciences. 44--66 (1995; Zbl 0900.17007)
Kashiwara, Masaki; Schmid, Wilfried Quasi-equivariant \({\mathcal D}\)-modules, equivariant derived category, and representations of reductive Lie groups. (English) Zbl 0854.22014 Brylinski, Jean-Luc (ed.) et al., Lie theory and geometry: in honor of Bertram Kostant on the occasion of his 65th birthday. Invited papers, some originated at a symposium held at MIT, Cambridge, MA, USA in May 1993. Boston, MA: Birkhäuser. Prog. Math. 123, 457-488 (1994). Reviewer: M.Muro (Yanagido) MSC: 22E45 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{W. Schmid}, Prog. Math. 123, 457--488 (1994; Zbl 0854.22014)
Kashiwara, Masaki; Nakashima, Toshiki Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras. (English) Zbl 0808.17005 J. Algebra 165, No. 2, 295-345 (1994). Reviewer: H.Yamada (Tokyo) MSC: 17B37 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Nakashima}, J. Algebra 165, No. 2, 295--345 (1994; Zbl 0808.17005) Full Text: DOI
Kashiwara, Masaki \(D\)-modules and representation theory of Lie groups. (English) Zbl 0823.22013 Ann. Inst. Fourier 43, No. 5, 1597-1618 (1993). Reviewer: V.Lakshmibai (Boston) MSC: 22E46 14M15 22E45 14L35 PDFBibTeX XMLCite \textit{M. Kashiwara}, Ann. Inst. Fourier 43, No. 5, 1597--1618 (1993; Zbl 0823.22013) Full Text: DOI Numdam EuDML
Kashiwara, Masaki Crystallizing of quantum groups. (Japanese) Zbl 0785.17016 Sūgaku 44, No. 4, 330-342 (1992). Reviewer: H.Yamada (Tokyo) MSC: 17B37 16W30 17-02 PDFBibTeX XMLCite \textit{M. Kashiwara}, Sūgaku 44, No. 4, 330--342 (1992; Zbl 0785.17016)
Kashiwara, Masaki Crystallization of quantized enveloping algebras. (English. Japanese original) Zbl 0797.17011 Sugaku Expo. 7, No. 1, 99-115 (1994); translation from Sugaku 44, No. 4, 330-342 (1992). MSC: 17B37 16W30 17-02 PDFBibTeX XMLCite \textit{M. Kashiwara}, Sugaku Expo. 7, No. 1, 99--115 (1992; Zbl 0797.17011); translation from Sugaku 44, No. 4, 330--342 (1992)
Kashiwara, Masaki Representation theory and D-modules on flag varieties. (English) Zbl 0705.22010 Orbites unipotentes et représentations. III. Orbites et faisceaux pervers, Astérisque 173-174, 55-109 (1989). Reviewer: M.Muro MSC: 22E45 14M15 32C38 14F10 17B35 22E60 PDFBibTeX XML
Kashiwara, Masaki The invariant holonomic system on a semisimple Lie group. (English) Zbl 0704.22008 Algebraic analysis, Pap. Dedicated to Prof. Mikio Sato on the Occas. of his Sixtieth Birthday, Vol. 1, 277-286 (1989). Reviewer: P.Godin MSC: 22E30 22E60 32C38 22E46 32A45 58J15 PDFBibTeX XML
Kashiwara, Masaki Character, character cycle, fixed point theorem and group representations. (English) Zbl 0699.22024 Representations of Lie groups: analysis on homogeneous spaces and representations of Lie groups, Proc. Symp., Kyoto/Jap. and Hiroshima/Jap. 1986, Adv. Stud. Pure Math. 14, 369-378 (1988). Reviewer: M.Muro MSC: 22E46 14L30 14L35 PDFBibTeX XML
Kashiwara, Masaki (ed.) An outline of D-modules. I, II. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto (Japan), October 27-29, 1986. (Japanese) Zbl 0695.32003 RIMS Kokyuroku, 667, 668. Kyoto: Kyoto University, Research Institute for Mathematical Sciences. iv, 204 p.; iv, 214 p. (1988). MSC: 32-06 00B25 32C38 58J10 22E47 13-06 PDFBibTeX XML
Hotta, R.; Kashiwara, M. Quotients of the Harish-Chandra system by primitive ideals. (English) Zbl 0576.22019 Geometry today, Int. Conf., Rome 1984, Prog. Math. 60, 185-205 (1985). Reviewer: I.Chekalov MSC: 22E47 22E46 35A30 17B35 PDFBibTeX XML
Kashiwara, Masaki The universal Verma module and the b-function. (English) Zbl 0574.17005 Algebraic groups and related topics, Proc. Symp., Kyoto and Nagoya/Jap. 1983, Adv. Stud. Pure Math. 6, 67-81 (1985). Reviewer: M.Muro MSC: 17B10 17B45 22E46 22E10 PDFBibTeX XML
Kashiwara, M.; Tanisaki, T. The characteristic cycles of holonomic systems on a flag manifold related to the Weyl group algebra. (English) Zbl 0611.22008 Invent. Math. 77, 185-198 (1984). Reviewer: W.Rossmann MSC: 22E46 22E47 17B10 22E45 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Tanisaki}, Invent. Math. 77, 185--198 (1984; Zbl 0611.22008) Full Text: DOI EuDML
Hotta, R.; Kashiwara, M. The invariant holonomic system on a semisimple Lie algebra. (English) Zbl 0538.22013 Invent. Math. 75, No. 2, 327-358 (1984). Reviewer: David Vogan MSC: 22E46 14F10 32C38 35Q15 PDFBibTeX XMLCite \textit{R. Hotta} and \textit{M. Kashiwara}, Invent. Math. 75, 327--358 (1984; Zbl 0538.22013) Full Text: DOI EuDML
Brylinski, J. L.; Kashiwara, M. Kazhdan-Lusztig conjecture and holonomic systems. (English) Zbl 0473.22009 Invent. Math. 64, 387-410 (1981). MSC: 22E47 14F40 14L30 35A99 55N35 PDFBibTeX XMLCite \textit{J. L. Brylinski} and \textit{M. Kashiwara}, Invent. Math. 64, 387--410 (1981; Zbl 0473.22009) Full Text: DOI EuDML
Brylinski, Jean-Luc; Kashiwara, Masaki Demonstration de la conjecture de Kazhdan-Lusztig sur les modules de Verma. (French) Zbl 0457.22012 C. R. Acad. Sci., Paris, Sér. A 291, 373-376 (1980). MSC: 22E47 14M15 35N99 55N99 PDFBibTeX XMLCite \textit{J.-L. Brylinski} and \textit{M. Kashiwara}, C. R. Acad. Sci., Paris, Sér. A 291, 373--376 (1980; Zbl 0457.22012)
Kashiwara, M.; Vergne, M. K-types and singular spectrum. (English) Zbl 0411.22015 Non-commutative harmonic analysis, Proc., Marseille-Luminy 1978, Lect. Notes Math. 728, 177-200 (1979). MSC: 22E46 46F15 PDFBibTeX XML
Kashiwara, Masaki; Vergne, Michele The Campbell-Hausdorff formula and invariant hyperfunctions. (English) Zbl 0404.22012 Invent. Math. 47, 249-272 (1978). Reviewer: François Rouvière MSC: 22E45 17B30 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{M. Vergne}, Invent. Math. 47, 249--272 (1978; Zbl 0404.22012) Full Text: DOI EuDML
Kashiwara, M.; Vergne, M. On the Segal-Shale-Weil representations and harmonic polynomials. (English) Zbl 0375.22009 Invent. Math. 44, 1-47 (1978). MSC: 22E45 22E30 32M15 43A32 43A85 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{M. Vergne}, Invent. Math. 44, 1--47 (1978; Zbl 0375.22009) Full Text: DOI EuDML
Kashiwara, Masaki; Vergne, Michèle Remarque sur la covariance de certains opérateurs différentiels. (French) Zbl 0366.22011 Non-commut. harmon. Anal., Actes Colloq., Marseille-Luminy 1976, Lect. Notes Math. 587, 119-137 (1977). Reviewer: F. Rouvière MSC: 22E45 81R20 58J90 PDFBibTeX XML