James' Submodule Theorem and the Steinberg Module

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Geck, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149266
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: James' Submodule Theorem and the Steinberg Module / M. Geck // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ.

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 o...