Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$
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| Format: | Preprint |
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2023
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| _version_ | 1866917947481522176 |
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| author | Cauchi, Antonio Terradillos, Armando Gutierrez |
| author_facet | Cauchi, Antonio Terradillos, Armando Gutierrez |
| contents | We study Shalika models for generic unramified representations of $\mathrm{PGU}_{2,2}$ over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. We then prove a Casselman-Shalika formula which relates the values of spherical Shalika functionals on ${\rm PGU}_{2,2}$ to the values of finite dimensional complex representations of the dual group of $\mathrm{PGSp}_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05759 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$ Cauchi, Antonio Terradillos, Armando Gutierrez Number Theory Representation Theory We study Shalika models for generic unramified representations of $\mathrm{PGU}_{2,2}$ over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. We then prove a Casselman-Shalika formula which relates the values of spherical Shalika functionals on ${\rm PGU}_{2,2}$ to the values of finite dimensional complex representations of the dual group of $\mathrm{PGSp}_4$. |
| title | Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2311.05759 |