Speh representations are relatively discrete

Abstract

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let ${\mathbf{Sp}}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\ge 2$. We prove that the Speh representations $\mathcal{U}(\delta ,2)$, where $\delta$ is a discrete series representation of ${\mathbf{GL}}_n(F)$, lie in the discrete spectrum of the $p$-adic symmetric space ${\mathbf{Sp}}_{2n}(F)\backslash {\mathbf{GL}}_{2n}(F)$.

30 pages, to appear in Represent. Theory; v3: Section 4.1 rewritten and Proposition 4.5 added, several minor errors corrected, bibliography updated

References in corpus (5)

• The dual group of a spherical variety
• Global Mixed Periods and local Klyachko models for the general linear group
• Relative discrete series representations for two quotients of $p$-adic ${\mathbf{GL}}_n$
• On Mœglin's parametrization of Arthur packets for p-adic quasisplit $Sp(N)$ and $SO(N)$
• Local unitary periods and relative discrete series