Generic weights for finite reductive groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908382708891648 |
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| author | Feng, Zhicheng Malle, Gunter Zhang, Jiping |
| author_facet | Feng, Zhicheng Malle, Gunter Zhang, Jiping |
| contents | This paper is motivated by the study of Alperin's weight conjecture in the representation theory of finite groups. We generalize the notion of $e$-cuspidality in the $e$-Harish-Chandra theory of finite reductive groups, and define generic weights in non-defining characteristic. We show that the generic weights play an analogous role as the weights defined by Alperin in the investigation of the inductive Alperin weight condition for simple groups of Lie type at most good primes. We hope that our approach will constitute a step towards an eventual proof of Alperin's weight conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic weights for finite reductive groups Feng, Zhicheng Malle, Gunter Zhang, Jiping Representation Theory Group Theory 20C33, 20C20, 20G40 This paper is motivated by the study of Alperin's weight conjecture in the representation theory of finite groups. We generalize the notion of $e$-cuspidality in the $e$-Harish-Chandra theory of finite reductive groups, and define generic weights in non-defining characteristic. We show that the generic weights play an analogous role as the weights defined by Alperin in the investigation of the inductive Alperin weight condition for simple groups of Lie type at most good primes. We hope that our approach will constitute a step towards an eventual proof of Alperin's weight conjecture. |
| title | Generic weights for finite reductive groups |
| topic | Representation Theory Group Theory 20C33, 20C20, 20G40 |
| url | https://arxiv.org/abs/2505.22064 |