Exhaustivity of unipotent representations for rigid orbits

Let $\mathcal U$ be the relevant set of rigid orbits, and suppose that $G(1)$ is not $O(l)$ for any $l\geq2$. Unipotent-exhaustivity conjecture. The set $\mathcal N(\mathcal O_{\bold D})$ exhausts all representations in $\Pi_{u,\mathcal O_{\bold D}}(G)$ for $Mp_{2n}(\mathbb R)$ and $O(p,q)$. This conjecture is proposed as one that would imply the preceding shortest-infinitesimal-character conjecture; it remains open in the paper.