4 problems

Intertwining-pole conjecture. One has

Generic-extension subrepresentation conjecture. The representation $\pi(C*D)$ is a subrepresentation of

Rigid-component conjecture. For $C\in\mathbf{Comp}(\mathbf{d})$, the induced representation $\pi(C)\times\pi(C)$ is irreducible if and only if $C$ contains an open $G_{\mathbf{d}}$…

Let $G=\operatorname{GL}_n(\mathbb{C})$, let $\mathbf{s}\in G^{\mathrm{rs}}$ be regular semisimple, and let $w,w'\in S_n$ be smooth permutations associated, via the natural combina…