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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.17401 |
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| _version_ | 1866908376224497664 |
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| author | Qin, Chuan |
| author_facet | Qin, Chuan |
| contents | We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's work. Our results for the finite case focus on the involution theorem for finite Hecke algebras that appear in Howlett-Lehrer's theory, where they proved a version for characters of certain subgroups of a Weyl group. We hope that our results will serve as a stepping stone for the study of involution for an arbitrary Bernstein block in the p-adic reductive group case. We also prove their compatibility with the Alvis-Curtis-Kawanaka duality (Aubert-Zelevinsky duality) when restricted to some Harish-Chandra series (resp. Bernstein blocks). This article is part of the author's PhD thesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An involution for Hecke algebras Qin, Chuan Representation Theory We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's work. Our results for the finite case focus on the involution theorem for finite Hecke algebras that appear in Howlett-Lehrer's theory, where they proved a version for characters of certain subgroups of a Weyl group. We hope that our results will serve as a stepping stone for the study of involution for an arbitrary Bernstein block in the p-adic reductive group case. We also prove their compatibility with the Alvis-Curtis-Kawanaka duality (Aubert-Zelevinsky duality) when restricted to some Harish-Chandra series (resp. Bernstein blocks). This article is part of the author's PhD thesis. |
| title | An involution for Hecke algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.17401 |