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arXiv · 2311.05759

Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$

Antonio Cauchi·Armando Gutierrez Terradillos
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Abstract

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 $\mathrm{PGSp}_4$.

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Antonio Cauchi, Armando Gutierrez Terradillos. 2023-11-09. Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. https://arxiv.org/abs/2311.05759

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