  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
$X$.
