James' Submodule Theorem and the Steinberg Module

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...

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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
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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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Geck, M.
author_facet Geck, M.
citation_txt James' Submodule Theorem and the Steinberg Module / M. Geck // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2025-12-07T21:10:16Z
format Article
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id nasplib_isofts_kiev_ua-123456789-149266
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T21:10:16Z
publishDate 2017
publisher Інститут математики НАН України
record_format dspace
spelling Geck, M.
2019-02-19T19:32:10Z
2019-02-19T19:32:10Z
2017
James' Submodule Theorem and the Steinberg Module / M. Geck // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 20C33; 20C20
DOI:10.3842/SIGMA.2017.091
https://nasplib.isofts.kiev.ua/handle/123456789/149266
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.
This paper is a contribution to the Special Issue on the Representation Theory of the Symmetric Groups
 and Related Topics. The full collection is available at https://www.emis.de/journals/SIGMA/symmetric-groups2018.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
James' Submodule Theorem and the Steinberg Module
Article
published earlier
spellingShingle James' Submodule Theorem and the Steinberg Module
Geck, M.
title James' Submodule Theorem and the Steinberg Module
title_full James' Submodule Theorem and the Steinberg Module
title_fullStr James' Submodule Theorem and the Steinberg Module
title_full_unstemmed James' Submodule Theorem and the Steinberg Module
title_short James' Submodule Theorem and the Steinberg Module
title_sort james' submodule theorem and the steinberg module
url https://nasplib.isofts.kiev.ua/handle/123456789/149266
work_keys_str_mv AT geckm jamessubmoduletheoremandthesteinbergmodule