Linear periods and distinguished local parameters

Abstract

Let $F$ be a nonarchimedean local field of characteristic zero and odd residual characteristic. Let $X$ be the $p$-adic symmetric space $X=H\backslash G$, where $G={\mathbf{GL}}_{2n}(F)$ and $H={\mathbf{GL}}_n(F)\times {\mathbf{GL}}_n(F)$. We verify a conjecture of Sakellaridis and Venkatesh on the Langlands parameters of certain representations in the discrete spectrum of $X$.

11 pages, to appear in Int. J. Number Theory, v4: exposition in section 1 streamlined; minor errors corrected; references updated

References in corpus (4)

• On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad
• The dual group of a spherical variety
• Relative discrete series representations for two quotients of $p$-adic ${\mathbf{GL}}_n$
• Local unitary periods and relative discrete series