Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914952172797952 |
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| author | Fry, A. A. Schaeffer Taylor, Jay Vinroot, C. Ryan |
| author_facet | Fry, A. A. Schaeffer Taylor, Jay Vinroot, C. Ryan |
| contents | We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this situation, we show that there is a unique Jordan decomposition satisfying conditions analogous to those of Digne--Michel's unique Jordan decomposition in the connected center case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00237 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer Fry, A. A. Schaeffer Taylor, Jay Vinroot, C. Ryan Group Theory Representation Theory 20C33 We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this situation, we show that there is a unique Jordan decomposition satisfying conditions analogous to those of Digne--Michel's unique Jordan decomposition in the connected center case. |
| title | Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer |
| topic | Group Theory Representation Theory 20C33 |
| url | https://arxiv.org/abs/2310.00237 |