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

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 $\mathrm{ PGSp}_4$.

Categories: math.NT math.RT