Let $E/F$ be a quadratic field extension of p-adic fields. Let $V$ be a (skew-)Hermitian space and $U(V)$ be the unitary group. Let $GU(V)$ be the similitude unitary group. Given an irreducible smooth representation $\pi$ of $GU(V)$, do we know that the restriction $\pi|_{U(V)}$ has multiplicity one?

For the pair $(GL(n),SL(n))$ similar results are proved by Tadic. For the pair $(GSp, Sp)$, similar results are proved by Adler-Prasad. I am wondering if the unitary group version is true or not.

Thanks.