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Let $\rho$ is a cuspidal representation of $GL(n,F)$, with $F$ a nonarchimedean local field, and $H$ a maximal Levi subgroup of $GL(n,F)$. We showthat if $\rho$ is $H$-distinguished, then $n$ is even, and $H\simeqGL(n/2,F)\times GL(n/2,F)$.

Cuspidal representations of $GL(n,F)$ distinguished by a maximal Levi subgroup, with $F$ a non-archimedean local field