Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras

被引：18
作者：
Shan, P.
Varagnolo, M.
Vasserot, E.
机构：
来源：
ADVANCES IN MATHEMATICS | 2014年 / 262卷
关键词：
Koszul duality; Affine Kac-Moody algebras; Cherednik algebras; MOMENT GRAPHS; LOCALIZATION; TRANSLATION; CATEGORY; FUNCTORS;
D O I：
10.1016/j.aim.2014.05.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affine Schubert varieties. We apply this duality to q-Schur algebras and to cyclotomic rational double affine Hecke algebras. This yields a proof of a conjecture of Chuang-Miyachi relating the level-rank duality with the Ringel-Koszul duality of cyclotomic rational double affine Hecke algebras. (C) 2014 Elsevier Inc. All rights reserved.
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收藏
页码：370 / 435
页数：66
相关论文
共 43 条
[1]  
Achar P. N., ARXIV11052181
[2]   Quasi-hereditary extension algebras [J].
Agoston, I ;
Dlab, V ;
Lukács, E .
ALGEBRAS AND REPRESENTATION THEORY, 2003, 6 (01) :97-117
[3]  
[Anonymous], 1991, J. Amer. Math. Soc.
[4]  
Backelin E., 1999, Represent. Theory, V3, P139
[5]   Koszul duality patterns in representation theory [J].
Beilinson, A ;
Ginzburg, V ;
Soergel, W .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) :473-527
[6]  
Beilinson A., QUANTIZATION H UNPUB
[7]  
Bezrukavnikov R., ARXIV11011253V1
[8]  
Braden T, 2001, MATH ANN, V321, P533
[9]  
Carter R. W., 1985, FINITE GROUPS LIE TY
[10]  
Chuang J., PREPRINT
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