On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915018853842944 |
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| author | Zelingher, Elad |
| author_facet | Zelingher, Elad |
| contents | We establish a relation between Speh representations of $\mathrm{GL}_n\left(\mathbb{F}_q\right)$ and Speh representations of $\mathrm{GL}_n\left(F\right)$, where $F$ is a non-archimedean local field. We use irreducible level zero supercuspidal representations to show that these two notions of Speh representations associated to cuspidal representations are related via a commutative diagram, and that their corresponding $(k,c)$ $ψ$-Whittaker models are also related. We use these results to relate the local Ginzburg-Kaplan integrals for level zero supercuspidal representations to their finite field counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors Zelingher, Elad Representation Theory Number Theory 11F70, 11F66, 20C33, 22E50 We establish a relation between Speh representations of $\mathrm{GL}_n\left(\mathbb{F}_q\right)$ and Speh representations of $\mathrm{GL}_n\left(F\right)$, where $F$ is a non-archimedean local field. We use irreducible level zero supercuspidal representations to show that these two notions of Speh representations associated to cuspidal representations are related via a commutative diagram, and that their corresponding $(k,c)$ $ψ$-Whittaker models are also related. We use these results to relate the local Ginzburg-Kaplan integrals for level zero supercuspidal representations to their finite field counterparts. |
| title | On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors |
| topic | Representation Theory Number Theory 11F70, 11F66, 20C33, 22E50 |
| url | https://arxiv.org/abs/2408.01856 |