9 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.

Shahidi Conjecture. For any quasi-split reductive group $G$, every tempered $L$-packet 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 $bbG$ 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 $bbpsi$…

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

Dual generic representation conjecture. One has

Let $G$ be a quasi-split connected reductive group over a local field $k$ of characteristic zero, let $G'$ be a pure inner form, and let $\Pi'_{\varphi}$ be the standard $L$-packet…

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…