Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution
We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q) in non-defining characteristic ℓ. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves b...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209457 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution / O. Dudas , N. Jacon // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696244366802944 |
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| author | Dudas, O. Jacon, N. |
| author_facet | Dudas, O. Jacon, N. |
| citation_txt | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution / O. Dudas , N. Jacon // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q) in non-defining characteristic ℓ. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves both ℓ and the order of q modulo ℓ.
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| first_indexed | 2025-12-07T16:26:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209457 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:26:26Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dudas, O. Jacon, N. 2025-11-21T19:13:05Z 2018 Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution / O. Dudas , N. Jacon // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C20; 20C30; 05E10 arXiv: 1706.04743 https://nasplib.isofts.kiev.ua/handle/123456789/209457 https://doi.org/10.3842/SIGMA.2018.007 We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q) in non-defining characteristic ℓ. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves both ℓ and the order of q modulo ℓ. The authors gratefully acknowledge financial support from the ANR grant GeRepMod ANR-16-CE40-0010-01. We thank Gunter Malle, Emily Norton, and the referees for their many valuable comments on a preliminary version of the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution Article published earlier |
| spellingShingle | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution Dudas, O. Jacon, N. |
| title | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution |
| title_full | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution |
| title_fullStr | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution |
| title_full_unstemmed | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution |
| title_short | Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution |
| title_sort | alvis-curtis duality for finite general linear groups and a generalized mullineux involution |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209457 |
| work_keys_str_mv | AT dudaso alviscurtisdualityforfinitegenerallineargroupsandageneralizedmullineuxinvolution AT jaconn alviscurtisdualityforfinitegenerallineargroupsandageneralizedmullineuxinvolution |