Deep level Deligne--Lusztig induction for tamely ramified tori
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908758897065984 |
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| author | Ivanov, Alexander B. Nie, Sian |
| author_facet | Ivanov, Alexander B. Nie, Sian |
| contents | Deep level Deligne--Lusztig representations, which are natural analogues of classical Deligne--Lusztig representations, recently play an important role in geometrization of irreducible supercuspidals of $p$-adic groups. In this paper, we propose a construction of deep level Deligne--Lusztig varieties/representations in the tamely ramified case, extending previous constructions in the unramified case. As an application, under a mild assumption on the residue field, we show that each regular irreducible supercuspidal is the compact induction of a deep level Deligne--Lusztig representation, and generally, each irreducible supercuspidal is a direct summand of the compact induction of the cohomology of a deep level Deligne--Lusztig variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deep level Deligne--Lusztig induction for tamely ramified tori Ivanov, Alexander B. Nie, Sian Representation Theory Algebraic Geometry Deep level Deligne--Lusztig representations, which are natural analogues of classical Deligne--Lusztig representations, recently play an important role in geometrization of irreducible supercuspidals of $p$-adic groups. In this paper, we propose a construction of deep level Deligne--Lusztig varieties/representations in the tamely ramified case, extending previous constructions in the unramified case. As an application, under a mild assumption on the residue field, we show that each regular irreducible supercuspidal is the compact induction of a deep level Deligne--Lusztig representation, and generally, each irreducible supercuspidal is a direct summand of the compact induction of the cohomology of a deep level Deligne--Lusztig variety. |
| title | Deep level Deligne--Lusztig induction for tamely ramified tori |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2601.06929 |