A pair of groups $(G,H)$ is called a symmetric pair if $H$ is the group of fixed points of an involutive automorphism of $G$, for example $(GL(2n,\mathbb{F}_q),Sp(2n,\mathbb{F_q}))$ is a symmetric pair with respect to the involution $\theta(A)=J(A^{-1})^tJ^{-1}$ where:

$$ J=\left(\begin{array}{cc} 0&id_n\\-id_n&0 \end{array}\right) $$

We also say that a pair $(G,K)$ where $K$ is a subgroup of $G$ is a Gelfand pair if for any irreducible representation $\pi$ of $G$, we have that $\pi^K$ (the vectors fixed by $K$) is at most one dimensional. Alternatively, $Hom_K(\pi, 1)\leq 1$.

It is known that many symmetric pairs of finite groups of lie type are Gelfand pairs, as in many we have that an associated anti-involution $\sigma(x)=\theta(x^{-1})$ preserves $H-H$ double cosets. I was wondering if it was known that any such symmetric pair of finite groups of Lie type is a Gelfand pair, or if there is a known counterexample to that assertion.