7 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…

Mod-Gaussian fluctuation conjecture. This singular point corresponds to mod-Gaussian fluctuations, but with parameters $N_{n,k}$ and $D_{n,k}$ different from those in the generic c…

Let $M$ be an $F$-Levi subgroup and let $\Pi_{\widetilde{\sigma}}(M(F))$ be a family of representations that can be considered as an $L$-packet on $M$. For…

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…

Vershik–Kerov's pointwise conjecture. For $\mathbb{Pl}$-almost every path … we have

Vershik–Kerov's conjecture. The sequence of random variables