Some remarks on Gill's theorems on Young modules

JOURNAL OF ALGEBRA

卷:430

Article

Donkin, Stephen

关键词: Representations;    Symmetric groups;    Hecke algebras;    Young modules;   

DOI  :  10.1016/j.jalgebra.2014.12.045

来源: Elsevier

【 摘 要 】

In a recent paper, [10], Gill, using methods of the modular representation theory of finite groups, describes some results on the tensor product of Young modules for symmetric groups. We here give an alternative approach using the polynomial representation theory of general linear groups and the Schur functor. The main result is a formula for the multiplicities of Young modules in a tensor product in terms of the characters of the simple polynomial modules for general linear groups. Our approach is also valid for Young modules for Hecke algebras of type A at roots of unity and here the formula involves the characters of the simple polynomial modules for quantised general linear groups. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free