Tadić's preservation of unitarizability conjecture

Let $G_n$ be a classical group, let $\pi\in\Pi(G_n)$ be weakly real, and suppose its decomposition involves the representations $X_{\rho_i}(\pi)$ for $i=1,\ldots,r$.

Tadić's preservation of unitarizability conjecture. If $\pi\in\Pi(G_n)$ is weakly real, then $\pi$ is unitary if and only if $X_{\rho_i}(\pi)$ is unitary for every $i=1,\ldots,r$.

This asks whether unitarity can be reduced to the corresponding smaller-rank representations. The paper presents it as a natural question and does not state that it is resolved in general.