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arXiv · 1708.07782

James' Submodule Theorem and the Steinberg Module

Meinolf Geck
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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 $BN$-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.

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Meinolf Geck. 2017-08-25. James' Submodule Theorem and the Steinberg Module. https://doi.org/10.3842/sigma.2017.091

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