Generic representations of finite general linear groups in cross characteristic
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916111478423552 |
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| author | Djament, Aurélien Gaujal, Thomas |
| author_facet | Djament, Aurélien Gaujal, Thomas |
| contents | We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We obtain especially a classification of such simple representations, what allows to prove a conjecture of Djament-Touz{é}-Vespa on dimensions taken by such a functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generic representations of finite general linear groups in cross characteristic Djament, Aurélien Gaujal, Thomas Category Theory K-Theory and Homology Representation Theory We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We obtain especially a classification of such simple representations, what allows to prove a conjecture of Djament-Touz{é}-Vespa on dimensions taken by such a functor. |
| title | Generic representations of finite general linear groups in cross characteristic |
| topic | Category Theory K-Theory and Homology Representation Theory |
| url | https://arxiv.org/abs/2305.02581 |