On two definitions of wave-front sets for $p$-adic groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912662797942784 |
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| author | Tsai, Cheng-Chiang |
| author_facet | Tsai, Cheng-Chiang |
| contents | The wave-front set for an irreducible admissible representation of a $p$-adic reductive group is the set of maximal nilpotent orbits which appear in the local character expansion. By Mœglin-Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are non-zero. However, in the literature there are two versions commonly used, one defining maximality using analytic closure and the other using Zariski closure. We show that these two definitions are non-equivalent for $G=Sp_4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_09536 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On two definitions of wave-front sets for $p$-adic groups Tsai, Cheng-Chiang Representation Theory Number Theory The wave-front set for an irreducible admissible representation of a $p$-adic reductive group is the set of maximal nilpotent orbits which appear in the local character expansion. By Mœglin-Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are non-zero. However, in the literature there are two versions commonly used, one defining maximality using analytic closure and the other using Zariski closure. We show that these two definitions are non-equivalent for $G=Sp_4$. |
| title | On two definitions of wave-front sets for $p$-adic groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2306.09536 |