27 problems

Jiang Conjecture. The following hold: (1) if a partition $\underline p$ is not related to $\eta_{\widehat{\mathfrak g}_n,\mathfrak g_n}(\underline p(\psi))$, then…

Let $F$ be a local field of characteristic zero, let $G$ be a classical group over $F$, and let $\pi\in\Pi_F(G)$ have a generic local $L$-parameter. For each symbol $\square$, let…

Let $\pi$ be a tempered unipotent representation of $\mathrm{SO}_{2n+1}(F)$, and let $\phi_{\hat \pi}$ be the $L$-parameter attached to its Aubert dual. Write…

Let $G$ be a $p$-adic group, let $\bar G^{(u)}$ be a $u$-fold cover of $G$, and let $\pi$ be an irreducible genuine smooth representation of $\bar G^{(u)}(\BQ_p)$. Let…

Let $F$ be a local field of characteristic zero, let $G$ be a classical group over $F$, and let $\pi\in\Pi_F(G)$ have a generic local $L$-parameter. Let…

Let $G$ be a real reductive group and let $\pi$ be an irreducible Casselman–Wallach representation of $G$. Let $\operatorname{WF}_{\mathrm{tr}}(\pi)$ denote its analytic wavefront…

Let $G$ be a reductive Lie group and let $\pi$ be a Harish-Chandra module representation of $G$. Denote by $\operatorname{AV}(\pi)$ its associated variety and by…

The wavefront-set upper-bound conjecture. For any $\underline{p}\in\frak{p}^m(\tilde{\pi}_{\psi})$,

Let $H$ be a split classical group over $F$, let $u$ denote the nilpotent orbit of the image of … under the derivative of the relevant $\mathrm{SL}_2(\mathbb{C})$-factor, and let…

One-step geometric wavefront set speculation. Either

Let $G$ be a reductive group over a local field $F$, and let $\overline{G}^{(n)}$ be a Brylinski–Deligne cover of $G$. Write $\operatorname{Irr}_{\rm gen}(\overline{G}^{(n)})$ for…

Let $\pi=\pi(\lambda,s,{{\mathcal O}}^\vee_{\lambda,s},{{\mathcal L}}^\vee)$ be an irreducible representation in the tempered $L$-packet…

Supercuspidal wavefront-set conjecture. One has

Let ${\mathbf G}^\omega({\mathsf k})$ be a reductive $p$-adic group, let $\pi(\lambda,s,{{\mathcal O}}^\vee,{{\mathcal L}}^\vee)$ be an irreducible representation in the $L$-packet…

Let $G=\mathrm G(F)$, where $\mathrm G$ is a connected reductive algebraic group defined over $F$ and inner to a split group. Let ${}^{K}\mathrm{WF}(\pi)$ denote the unramified can…

Let $\mathrm G$ be a connected reductive group and let $G=\mathrm G(F)$. Assume the local Langlands correspondence for $G$. For a local $L$-parameter $\phi$, let $\Pi_\phi$ be its…

Let $\mathrm G$ be a connected reductive group and let $G=\mathrm G(F)$. Assume the local Langlands correspondence for $G$. For a local $L$-parameter $\phi$, let $\Pi_\phi$ be its…

Let $\mathrm G$ be a connected reductive group over $F$ with a quasi-split pure inner form, and let $G=\mathrm G(F)$. Let $\Phi(G)$ be the set of local $L$-parameters, let…

Let $G=\mathrm{G}(F)$ be the group of $F$-points of a connected reductive group, and assume the local Langlands correspondence for irreducible admissible representations of $G$. Le…

The weak local Arthur packets conjecture. The set $\Pi_{\psi}^{\textrm{Weak}}$ is a union of local Arthur packets.

Sommers' conjecture. The set $^K\WF(X)$ is a singleton and

Let $\psi$ be an Arthur parameter for a reductive group $\mathbf G$ over a nonarchimedean local field ${\mathsf k}$, and let $\mathcal O^{\vee}_{\psi}$ be the nilpotent $G^{\vee}$-…

Let $F$ be a local field of characteristic zero, let $G_n^*$ be an $F$-quasisplit classical group of the form $\operatorname{Isom}(V,q)^\circ$ for a non-degenerate $\epsilon$-Hermi…

Let $\mathbf{G}$ be a connected semisimple algebraic group over a $p$-adic field $\mathsf{k}$, and let $X$ be an irreducible admissible representation of…

Global coherence of wavefront sets. There should exist a coadjoint orbit depending on $\pi$,