On certain 𝑆𝑝-distinguished principal series representations of the quasi-split unitary groups

Mitra, Arnab

doi:10.1090/proc/15817

On certain $\mathrm {Sp}$-distinguished principal series representations of the quasi-split unitary groups
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Proc. Amer. Math. Soc. 150 (2022), 857-870 Request permission

Abstract:

Let $U_{2n}$ denote the quasi-split unitary group over $2n$ variables with respect to a quadratic extension $E/F$ of non-archimedean local fields. We study unitarizable principal series representations of $U_{2n}$, namely the irreducible unitarizable representations of $U_{2n}$ that are obtained via parabolic induction, from the point of view of distinction by the subgroup $\mathrm {Sp}_{2n}(F)$. After obtaining some results on distinction, we investigate the behavior of a certain class of principal series representations under the base change map which takes irreducible representations of $U_{2n}$ to those of $\operatorname {GL}_{2n}(E)$.

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