Spherical functions on symmetric spaces of Friedberg-Jacquet type
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910016898859008 |
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| author | Corato-Zanarella, Murilo |
| author_facet | Corato-Zanarella, Murilo |
| contents | We give explicit models for spherical functions on $p$-adic symmetric spaces $X=H\backslash G$ for pairs of $p$-adic groups $(G,H)$ of the form $(\mathrm{U}(2r),\mathrm{U}(r)\times \mathrm{U}(r)),$ $(\mathrm{O}(2r),\mathrm{O}(r)\times \mathrm{O}(r)),$ $(\mathrm{Sp}(4r),\mathrm{Sp}(2r)\times\mathrm{Sp}(2r))),$ $(\mathrm{U}(2r+1),\mathrm{U}(r+1)\times \mathrm{U}(r)),$ and $ (\mathrm{O}(2r+1),\mathrm{O}(r+1)\times \mathrm{O}(r)).$ As an application, we completely describe their Hecke module structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00148 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spherical functions on symmetric spaces of Friedberg-Jacquet type Corato-Zanarella, Murilo Number Theory Representation Theory We give explicit models for spherical functions on $p$-adic symmetric spaces $X=H\backslash G$ for pairs of $p$-adic groups $(G,H)$ of the form $(\mathrm{U}(2r),\mathrm{U}(r)\times \mathrm{U}(r)),$ $(\mathrm{O}(2r),\mathrm{O}(r)\times \mathrm{O}(r)),$ $(\mathrm{Sp}(4r),\mathrm{Sp}(2r)\times\mathrm{Sp}(2r))),$ $(\mathrm{U}(2r+1),\mathrm{U}(r+1)\times \mathrm{U}(r)),$ and $ (\mathrm{O}(2r+1),\mathrm{O}(r+1)\times \mathrm{O}(r)).$ As an application, we completely describe their Hecke module structure. |
| title | Spherical functions on symmetric spaces of Friedberg-Jacquet type |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2311.00148 |