Quiver Hecke Algebras and 2-Lie Algebras

被引：93
作者：
Rouquier, Raphael [1 ,2 ]
机构：
[1] Univ Oxford, Math Inst, Oxford OX1 3LB, England
[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
来源：
ALGEBRA COLLOQUIUM | 2012年 / 19卷 / 02期
关键词：
Lie algebras; Hecke algebras; representations; quiver varieties; QUANTUM; CATEGORIFICATION; SL(2);
D O I：
10.1142/S1005386712000247
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.
引用
收藏
页码：359 / 410
页数：52
相关论文
共 50 条
  • [1] ON THE CENTER OF QUIVER HECKE ALGEBRAS
    Shan, P.
    Varagnolo, M.
    Vasserot, E.
    DUKE MATHEMATICAL JOURNAL, 2017, 166 (06) : 1005 - 1101
  • [2] Localizations for quiver Hecke algebras
    Kashiwara, Masaki
    Kim, Myungho
    Oh, Se-Jin
    Park, Euiyong
    PURE AND APPLIED MATHEMATICS QUARTERLY, 2021, 17 (04) : 1465 - 1548
  • [3] A remark on convolution products for quiver Hecke algebras
    Kim, Myungho
    Park, Euiyong
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2020, 31 (11)
  • [4] Localizations for quiver Hecke algebras II
    Kashiwara, Masaki
    Kim, Myungho
    Oh, Se-jin
    Park, Euiyong
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2023, 127 (04) : 1134 - 1184
  • [5] Notes on parameters of quiver Hecke algebras
    Kashiwara, Masaki
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2012, 88 (07) : 97 - 102
  • [6] SYMPLECTIC DIRAC OPERATORS FOR LIE ALGEBRAS AND GRADED HECKE ALGEBRAS
    Ciubotaru, D.
    De Martino, M.
    Meyer, P.
    TRANSFORMATION GROUPS, 2023, 28 (04) : 1447 - 1475
  • [7] CYCLOTOMIC QUIVER HECKE ALGEBRAS CORRESPONDING TO MINUSCULE REPRESENTATIONS
    Park, Euiyong
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (06) : 1373 - 1388
  • [8] Specht Modules for Quiver Hecke Algebras of Type C
    Ariki, Susumu
    Park, Euiyong
    Speyer, Liron
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2019, 55 (03) : 565 - 626
  • [9] Quiver Hecke algebras for Borcherds-Cartan datum
    Tong, Bolun
    Wu, Wan
    JOURNAL OF ALGEBRA, 2023, 630 : 38 - 55
  • [10] Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras III
    Kang, Seok-Jin
    Kashiwara, Masaki
    Kim, Myungho
    Oh, Se-jin
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 420 - 444
12345