On reducibility of induced representations of odd unitary groups: the depth zero case

Abstract

We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to ${\mathrm{GL}}_n(E)\times {\mathrm{U}}_1(E)$. Let $\pi$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation ${\iota }_P^G\pi$ is reducible.

39 pages. arXiv admin note: substantial text overlap with arXiv:2005.03386