Speh representations are relatively discrete

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let ${\mathbf{S}\mathbf{p}}_{2n}(F)$ 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 ${\mathbf{G}\mathbf{L}}_n(F)$, lie in the discrete spectrum of the $p$-adic symmetric space ${\mathbf{S}\mathbf{p}}_{2n}(F)\mathrm{\backslash }{\mathbf{G}\mathbf{L}}_{2n}(F)$.