11 problems

Enhanced Shahidi Conjecture. For any quasi-split reductive group $G$, a local Arthur packet is tempered if and only if it has a generic member.

Suppose $bbG$ is $bbF$-quasi-split and fix a Whittaker datum $(bbU,bbpsi)$. An extended $L$-packet is a fibre of the composite semisimplification map from representations to semisi…

Let $r$ be a semisimple parameter. Gross–Prasad–Rallis maximal-monodromy conjecture. Up to $bbhat{bbG}$-conjugacy, there is a unique Langlands parameter $bbphi$ whose $L$-packet co…

Let $bbG$ be a connected reductive group over $bbF$, let $bbphi$ be an $bbSL_2$-parameter, and let $L(s,bboperatorname{Ad}\circbbphi)$ denote its adjoint $L$-factor. Gross–Prasad–R…

Let $bbG$ be an $bbF$-quasi-split connected reductive group and fix a Whittaker datum $(bbU,bbpsi)$. Tempered packet conjecture. Every tempered $L$-packet contains a unique $bbpsi$…

Let $k$ be a number field, let $\mathrm{G}$ be a connected reductive group over $k$, and let $\pi=\bigotimes_v\pi_v$ be an automorphic representation in the discrete spectrum of…

Let $G=\mathbf{G}(F)$ be a quasi-split group as above, let $\theta$ be a smooth character of the relevant subgroup, and let $\pi$ be an irreducible complex $\theta$-generic represe…

Gross-Prasad--Rallis conjecture. The parameter $phi$ is generic if and only if

Dual generic representation conjecture. One has

Let holomorphic paramodular cusp forms and holomorphic Siegel modular cusp forms be as in the source, and consider the local non-archimedean representations attached to the latter…

Let $G$ be a quasi-split connected reductive group over a local field $k$ of characteristic zero, with maximal torus $T$ and adjoint torus $T_{\operatorname{ad}}=T/Z$. Let…