James' Submodule Theorem and the Steinberg Module
Representation Theory
2017-12-06 v2
Abstract
James' submodule theorem is a fundamental result in the representation theory of the symmetric groups and the finite general linear groups. In this note we consider a version of that theorem for a general finite group with a split -pair. This gives rise to a distinguished composition factor of the Steinberg module, first described by Hiss via a somewhat different method. It is a major open problem to determine the dimension of this composition factor.
Cite
@article{arxiv.1708.07782,
title = {James' Submodule Theorem and the Steinberg Module},
author = {Meinolf Geck},
journal= {arXiv preprint arXiv:1708.07782},
year = {2017}
}