The generalized Gelfand–Graev characters of GLn(Fq)
Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6406/pdf |
| _version_ | 1797270200325767168 |
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| author | Scott Andrews Nathaniel Thiem |
| author_facet | Scott Andrews Nathaniel Thiem |
| author_sort | Scott Andrews |
| collection | DOAJ |
| description | Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. We use these alternate constructions to show how to obtain generalized Gelfand–Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand–Graev characters in terms of unipotent representations, thereby recovering the Kostka–Foulkes polynomials as multiplicities. |
| first_indexed | 2024-04-25T02:00:29Z |
| format | Article |
| id | doaj.art-5654c5ea4b554da7af06cd20110a70a8 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:29Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5654c5ea4b554da7af06cd20110a70a82024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.64066406The generalized Gelfand–Graev characters of GLn(Fq)Scott Andrews0Nathaniel Thiem1Boise State UniversityUniversity of Colorado [Boulder]Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. We use these alternate constructions to show how to obtain generalized Gelfand–Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand–Graev characters in terms of unipotent representations, thereby recovering the Kostka–Foulkes polynomials as multiplicities.https://dmtcs.episciences.org/6406/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Scott Andrews Nathaniel Thiem The generalized Gelfand–Graev characters of GLn(Fq) Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | The generalized Gelfand–Graev characters of GLn(Fq) |
| title_full | The generalized Gelfand–Graev characters of GLn(Fq) |
| title_fullStr | The generalized Gelfand–Graev characters of GLn(Fq) |
| title_full_unstemmed | The generalized Gelfand–Graev characters of GLn(Fq) |
| title_short | The generalized Gelfand–Graev characters of GLn(Fq) |
| title_sort | generalized gelfand graev characters of gln fq |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6406/pdf |
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