On Young modules of general linear groups

JOURNAL OF ALGEBRA

卷:310

Article

Erdmann, Karin ; Schroll, Sibylle

关键词: finite general linear groups;    Young modules;    Specht modules;    filtration multiplicities;    stratifying systems;   

DOI  :  10.1016/j.jalgebra.2006.11.004

来源: Elsevier

【 摘 要 】

We study e-permutation modules of finite general linear groups GL(n) (q) acting on partial flags in the natural module, where the coefficient field of the modules has characteristic E, for f inverted iota q. We call the indecomposable summands of these permutation modules linear Young modules. We determine their vertices and Green correspondents, by methods relying only on the representation theory of GLn (q). Furthermore, we show that when the multiplicative order of q modulo e is strictly greater than 1, the Specht modules for GL(n) (q) in characteristic f form a stratifying system. This implies in particular, that for GL(n) (q)-modules with Specht filtration, the filtration multiplicities are independent of the filtration. This is an analogue of a recent theorem by Hemmer and Nakano. (c) 2006 Elsevier Inc. All fights reserved.

【 授权许可】

Free