Local unitary periods and relative discrete series

Let $F$ be a $p$-adic field ($p\mathrm{\ne }2$), let $E$ be a quadratic Galois extension of $F$, and let $n\ge 2$. We construct representations in the discrete spectrum of the $p$-adic symmetric space $H\mathrm{\backslash }G$, where $G = $\mathbf{G}\mathbf{L}${2n}(E)$and$H = $\mathbf{U}${E/F}(F)$ is a quasi-split unitary group over $F$.