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 |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| 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| _version_ | 1862751140323524608 |
|---|---|
| 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.
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| first_indexed | 2025-12-07T21:10:16Z |
| format | Article |
| fulltext | |
| 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 |