SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS

被引：12

作者：

Andersen, Henning Haahr ^{[1
]}

Stroppel, Catharina ^{[2
]}

Tubbenhauer, Daniel ^{[3
]}

机构：

[1] Aarhus Univ, Ctr Quantum Geometry Moduli Spaces, Ny Munkegade 118,Bldg 1530,Room 327, DK-8000 Aarhus C, Denmark

[2] Univ Bonn, Math Inst, Endenicher Allee 60,Room 4-007, D-53115 Bonn, Germany

[3] Univ Bonn, Math Inst, Endenicher Allee 60,Room 1-003, D-53115 Bonn, Germany

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 103卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

quantum groups; (quantum) tilting modules; Jantzen's sum formulas; semisimplicity; Hecke and Brauer algebras; SCHUR-WEYL RECIPROCITY; ARIKI-KOIKE ALGEBRAS; QUANTUM GROUPS; CENTRALIZER ALGEBRAS; LIE-ALGEBRAS; REPRESENTATIONS; MODULES; CRITERION; DUALITY; THEOREM;

D O I：

10.1017/S1446788716000392

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show how to use Jantzen's sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of U-q-tilting modules (for any field K and any parameter q is an element of k - {0, -1}). As an application, we recover the semisimplicity criteria for the Hecke algebras of types A and B, the walled Brauer algebras and the Brauer algebras from our more general approach.

引用

页码：1 / 44

页数：44

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[1] ON THE SEMISIMPLICITY OF HECKE ALGEBRAS
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[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1989, 41 (01) : 75 - 79
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