Deep level Deligne--Lusztig representations of Coxeter type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910732252086272 |
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| author | Ivanov, Alexander B. Nie, Sian Tan, Panjun |
| author_facet | Ivanov, Alexander B. Nie, Sian Tan, Panjun |
| contents | In this article we study the cohomology of deep level Deligne--Lusztig varieties of Coxeter type, attached to a reductive group over a local non-archimedean field, which splits over an unramified extension. This allows to construct some new irreducible representations of parahoric subgroups of $p$-adic groups. Moreover, in the quasi-split case we prove that these compactly induce to finite direct sums of irreducible supercuspidal representations of the $p$-adic group. This extends previous results of \cite{DI}, \cite{CI_loopGLn}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep level Deligne--Lusztig representations of Coxeter type Ivanov, Alexander B. Nie, Sian Tan, Panjun Representation Theory Algebraic Geometry 20G05, 20G25, 20G40, 11G25 In this article we study the cohomology of deep level Deligne--Lusztig varieties of Coxeter type, attached to a reductive group over a local non-archimedean field, which splits over an unramified extension. This allows to construct some new irreducible representations of parahoric subgroups of $p$-adic groups. Moreover, in the quasi-split case we prove that these compactly induce to finite direct sums of irreducible supercuspidal representations of the $p$-adic group. This extends previous results of \cite{DI}, \cite{CI_loopGLn}. |
| title | Deep level Deligne--Lusztig representations of Coxeter type |
| topic | Representation Theory Algebraic Geometry 20G05, 20G25, 20G40, 11G25 |
| url | https://arxiv.org/abs/2407.18694 |