Muić's irreducibility conjecture for big theta lifts

Let $F$ be a non-archimedean local field of characteristic zero, let $G(W_n)$ and $H(V_m)$ be the members of a local theta-correspondence dual pair, and let $\theta(\pi)$ and $\Theta(\pi)$ denote respectively the small and big theta lifts of an irreducible discrete series representation $\pi$ of $G(W_n)$ to $H(V_m)$. The big theta lift is understood to be the full lift, while the small theta lift is its irreducible quotient when non-zero.

Muić's conjecture. The big theta lift $\Theta(\pi)$ to $H(V_m)$ is irreducible, if non-zero.

This conjecture extends Muić's result in the cases where the small theta lift of a discrete series representation is non-zero and tempered. The paper states that it proves the conjecture, so its status is recorded as solved.