The stable wave front set of theta representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910683442970624 |
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| author | Karasiewicz, Edmund Okada, Emile Wang, Runze |
| author_facet | Karasiewicz, Edmund Okada, Emile Wang, Runze |
| contents | We compute the stable wave front set of theta representations for certain tame Brylinski-Deligne covers of a connected reductive $p$-adic group. The computation involves two main inputs. First we use a theorem of Okada, adapted to covering groups, to reduce the computation of the wave front set to computing the Kawanaka wave front set of certain representations of finite groups of Lie type. Second, to compute the Kawanaka wave front sets we use Lusztig's formula. This requires a careful analysis of the action of the pro-$p$ Iwahori-Hecke algebra on the theta representation, using the structural results about Hecke algebras developed by Gao-Gurevich-Karasiewicz and Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stable wave front set of theta representations Karasiewicz, Edmund Okada, Emile Wang, Runze Representation Theory Number Theory 22E50 We compute the stable wave front set of theta representations for certain tame Brylinski-Deligne covers of a connected reductive $p$-adic group. The computation involves two main inputs. First we use a theorem of Okada, adapted to covering groups, to reduce the computation of the wave front set to computing the Kawanaka wave front set of certain representations of finite groups of Lie type. Second, to compute the Kawanaka wave front sets we use Lusztig's formula. This requires a careful analysis of the action of the pro-$p$ Iwahori-Hecke algebra on the theta representation, using the structural results about Hecke algebras developed by Gao-Gurevich-Karasiewicz and Wang. |
| title | The stable wave front set of theta representations |
| topic | Representation Theory Number Theory 22E50 |
| url | https://arxiv.org/abs/2411.02073 |