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
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