The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916124984082432 |
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| author | Ivanov, Alexander B. Nie, Sian |
| author_facet | Ivanov, Alexander B. Nie, Sian |
| contents | We determine the cohomology of the closed Drinfeld stratum of $p$-Deligne--Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree, and are pairwisely non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy--Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov's orbit method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type Ivanov, Alexander B. Nie, Sian Representation Theory Algebraic Geometry 20G05, 20G25, 20G40, 11G25 We determine the cohomology of the closed Drinfeld stratum of $p$-Deligne--Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree, and are pairwisely non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy--Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov's orbit method. |
| title | The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type |
| topic | Representation Theory Algebraic Geometry 20G05, 20G25, 20G40, 11G25 |
| url | https://arxiv.org/abs/2402.09017 |