On the modular composition factors of the Steinberg representation

JOURNAL OF ALGEBRA

卷:475

Article

Geck, Meinolf¹ 

[1] Univ Stuttgart, IAZ Lehrstuhl Algebra, Paffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Finite groups of Lie type;    Steinberg representation;    Hecke algebra;    Modular representations;   

DOI  :  10.1016/j.jalgebra.2015.11.005

来源: Elsevier

【 摘 要 】

Let G be a finite group of Lie type and St(kappa) be the Steinberg representation of G, defined over a field kappa. We are interested in the case where k has prime characteristic. and Stk is reducible. Tinberg has shown that the socle of Stk is always simple. We give a new proof of this result in terms of the Hecke algebra of G with respect to a Borel subgroup and show how to identify the simple socle of St(kappa) among the principal series representations of G. Furthermore, we determine the composition length of St(kappa) when G = GL(n)(q) or G is a finite classical group and l is a so-called linear prime. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free