Kashiwara, Masaki; Oh, Se-jin \(t\)-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras. (English) Zbl 07823123 Adv. Math. 441, Article ID 109551, 82 p. (2024). MSC: 16T30 17B37 17B67 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{S.-j. Oh}, Adv. Math. 441, Article ID 109551, 82 p. (2024; Zbl 07823123) Full Text: DOI arXiv
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; Kim, Myungho; Oh, Se-Jin; Park, Euiyong Simply laced root systems arising from quantum affine algebras. (English) Zbl 1512.17022 Compos. Math. 158, No. 1, 168-210 (2022). MSC: 17B37 17B22 17B67 18M05 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Compos. Math. 158, No. 1, 168--210 (2022; Zbl 1512.17022) Full Text: DOI arXiv
Kashiwara, Masaki; Kim, Myungho; Oh, Se-Jin; Park, Euiyong Monoidal categorification and quantum affine algebras. (English) Zbl 1497.17020 Compos. Math. 156, No. 5, 1039-1077 (2020). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 13F60 18N25 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Compos. Math. 156, No. 5, 1039--1077 (2020; Zbl 1497.17020) 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
Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin Monoidal categories of modules over quantum affine algebras of type \(A\) and \(B\). (English) Zbl 1472.17054 Proc. Lond. Math. Soc. (3) 118, No. 1, 43-77 (2019). Reviewer: Sonia Natale (Córdoba) MSC: 17B37 81R50 16T25 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Proc. Lond. Math. Soc. (3) 118, No. 1, 43--77 (2019; Zbl 1472.17054) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras. (English) Zbl 1407.81108 Invent. Math. 211, No. 2, 591-685 (2018); correction ibid. 216, No. 2, 597-599 (2019). Reviewer: Uwe Franz (Besançon) MSC: 17B37 16G20 16T25 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Invent. Math. 211, No. 2, 591--685 (2018; Zbl 1407.81108) 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
Grantcharov, Dimitar; Jung, Ji Hye; Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho Crystal bases for the quantum queer superalgebra. (English) Zbl 1336.17014 J. Eur. Math. Soc. (JEMS) 17, No. 7, 1593-1627 (2015). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B37 PDFBibTeX XMLCite \textit{D. Grantcharov} et al., J. Eur. Math. Soc. (JEMS) 17, No. 7, 1593--1627 (2015; Zbl 1336.17014) 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. 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
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato Tropical \(R\) maps and affine geometric crystals. (English) Zbl 1220.17006 Represent. Theory 14, 446-509 (2010). MSC: 17B37 17B67 22E65 14M15 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Represent. Theory 14, 446--509 (2010; Zbl 1220.17006) Full Text: DOI arXiv
Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato Affine geometric crystals and limit of perfect crystals. (English) Zbl 1219.17010 Trans. Am. Math. Soc. 360, No. 7, 3645-3686 (2008). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B37 17B67 22E65 14M15 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Trans. Am. Math. Soc. 360, No. 7, 3645--3686 (2008; Zbl 1219.17010) Full Text: DOI arXiv
Kashiwara, M.; Misra, K. C.; Okado, M.; Yamada, D. Perfect crystals for \(U_q(D_4^{(3)})\). (English) Zbl 1140.17012 J. Algebra 317, No. 1, 392-423 (2007). Reviewer: Jan Grabowski (Oxford) MSC: 17B37 17B67 81R50 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., J. Algebra 317, No. 1, 392--423 (2007; Zbl 1140.17012) Full Text: DOI arXiv
Kashiwara, Masaki; Tanisaki, Toshiyuki Parabolic Kazhdan-Lusztig polynomials and Schubert varieties. (English) Zbl 1021.17015 J. Algebra 249, No. 2, 306-325 (2002). Reviewer: Isidro Nieto Baños (Morelia) MSC: 17B67 14M15 14F43 PDFBibTeX XMLCite \textit{M. Kashiwara} and \textit{T. Tanisaki}, J. Algebra 249, No. 2, 306--325 (2002; Zbl 1021.17015) Full Text: arXiv
Benkart, Georgia; Kang, Seok-Jin; Kashiwara, Masaki Crystal bases for the quantum superalgebra \(U_q(\mathfrak{gl}(m,n))\). (English) Zbl 0963.17010 J. Am. Math. Soc. 13, No. 2, 295-331 (2000). Reviewer: Richard M.Green (Lancaster) MSC: 17B37 05E10 81R50 PDFBibTeX XMLCite \textit{G. Benkart} et al., J. Am. Math. Soc. 13, No. 2, 295--331 (2000; Zbl 0963.17010) 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, M.; Miwa, T.; Petersen, J.-U. H.; Yung, C. M. Perfect crystals and \(q\)-deformed Fock spaces. (English) Zbl 0959.17014 Sel. Math., New Ser. 2, No. 3, 415-499 (1996). MSC: 17B37 81R50 17B69 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Sel. Math., New Ser. 2, No. 3, 415--499 (1996; Zbl 0959.17014) 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, M.; Miwa, T.; Stern, E. Decomposition of \(q\)-deformed Fock spaces. (English) Zbl 0857.17013 Sel. Math., New Ser. 1, No. 4, 787-805 (1995). MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Sel. Math., New Ser. 1, No. 4, 787--805 (1995; Zbl 0857.17013) Full Text: DOI arXiv
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
Kang, Seok-Jin; Kashiwara, Masaki; Misra, Kailash C.; Miwa, Tetsuji; Nakashima, Toshiki; Nakayashiki, Atsushi Perfect crystals of quantum affine Lie algebras. (English) Zbl 0774.17017 Duke Math. J. 68, No. 3, 499-607 (1992). Reviewer: Ye Jiachen (Shanghai) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S.-J. Kang} et al., Duke Math. J. 68, No. 3, 499--607 (1992; Zbl 0774.17017) Full Text: DOI
Date, E.; Jimbo, M.; Kashiwara, M.; Miwa, T. Transformation groups of soliton equations. IV: A new hierarchy of soliton equations of KP-type. (English) Zbl 0571.35100 Physica D 4, No. 3, 343-365 (1982). MSC: 35Q99 17B65 22E65 PDFBibTeX XMLCite \textit{E. Date} et al., Physica D 4, No. 3, 343--365 (1982; Zbl 0571.35100) Full Text: DOI