Quantum Weyl Reciprocity and Tilting Modules

被引：0

作者：

Jie Du

Brian Parshall

Leonard Scott

机构：

[1] School of Mathematics,

[2] University of New South Wales,undefined

[3] Sydney 2052,undefined

[4] Australia,undefined

[5] Department of Mathematics,undefined

[6] University of Virginia,undefined

[7] Charlottesville,undefined

[8] VA 22903-3199,undefined

[9] USA,undefined

来源：

Communications in Mathematical Physics | 1998年 / 195卷

关键词：

Representation Theory; Laurent Polynomial; Interesting Situation; Quotient Algebra; Tilting Module;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Quantum Weyl reciprocity relates the representation theory of Hecke algebras of type A with that of q-Schur algebras. This paper establishes that Weyl reciprocity holds integrally (i. e., over the ring ℤ[q, q− 1] of Laurent polynomials) and that it behaves well under base-change. A key ingredient in our approach involves the theory of tilting modules for q-Schur algebras. New results obtained in that direction include an explicit determination of the Ringel dual algebra of a q-Schur algebra in all cases. In particular, in the most interesting situation, the Ringel dual identifies with a natural quotient algebra of the Hecke algebra.

引用

页码：321 / 352

页数：31