3 problems

Let $G$ be the reductive group under consideration, let $\operatorname{Temp}(G)$ be its tempered dual, and let $\pi\in\operatorname{Temp}(G)$. Let $\rho_{\pi,\varpi}$ be the repres…

Let $F$ be a nonarchimedean local field, let $G$ be the group of $F$-points of a reductive group, and let $P=MU$ be a parabolic subgroup with Levi factor $M$. Let…

Let $(\lambda^{(1)},\lambda^{(2)})$ be a random bipartition under the B-$q$-Plancherel measure, and let $\lambda=\lambda^{(1)}\sqcup\lambda^{(2)}$. Asymptotic part-allocation conje…