Spherical functions of symmetric forms and a conjecture of Hironaka
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908823601545216 |
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| author | Corato-Zanarella, Murilo |
| author_facet | Corato-Zanarella, Murilo |
| contents | For all $r\ge1,$ we verify the following conjecture of Hironaka: for a $p$-adic field $F$ with $p$ odd, the space of spherical functions of $\mathrm{Sym}_{r\times r}(F)\cap\mathrm{GL}_r(F)$ is free of rank $4^r$ over the Hecke algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spherical functions of symmetric forms and a conjecture of Hironaka Corato-Zanarella, Murilo Number Theory Representation Theory For all $r\ge1,$ we verify the following conjecture of Hironaka: for a $p$-adic field $F$ with $p$ odd, the space of spherical functions of $\mathrm{Sym}_{r\times r}(F)\cap\mathrm{GL}_r(F)$ is free of rank $4^r$ over the Hecke algebra. |
| title | Spherical functions of symmetric forms and a conjecture of Hironaka |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2311.00147 |