26 problems

Shahidi's conjecture. Every tempered $L$-packet contains a generic member.

Reeder's rational-ratio conjecture. The formal dimensions of the unipotent discrete series representations of $\mathcal{G}$ within one unipotent discrete series $L$-packet are prop…

Internal parametrization conjecture. There exists a canonical surjection

Kaletha's internal parametrization conjecture. The packet on $(G',\iota,z)$ should be internally labeled by

Let $F$ be a nonarchimedean local field, let $G$ be the group of $F$-points of a connected reductive group, let $\Phi(G)$ be the set of equivalence classes of Langlands parameters…

Let $G$ be a quasi-split connected reductive group over a local or global field $F$. For a parameter $\mathfrak{psi}$, let $mathit{Pi}_{\mathfrak{psi}}(G)^A$ and…

p-adic analogue conjecture. These properties should hold in the $p$-adic case as well.

Let $G_n$ be the group considered in the paper, let $\psi$ be a local Arthur parameter, let $\widetilde\Pi^J_\psi$ be the Jiang packet, let $\widehat\Pi_{\phi_{\widehat\psi}}$ be t…

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 $G=\operatorname{GSp}_4\times\operatorname{GL}_2\times\operatorname{GL}_2$ with $H=(\operatorname{GL}_2\times\operatorname{GL}_2)^0$, let $(G_D,H_D)$ be its quaternionic inner…

Fix a local field $F$, a model $(G,H)$ in the paper's table, a tempered $L$-parameter $\phi$, its component group $S_\phi$, and the representation $\rho_X$ attached to the spherica…

For $\theta \in \Sigma_0$ and a semisimple element $s \in \bar{S}_{\phi}^{\theta}$, let $(G',\phi') \rightarrow (\phi,s)$ be the corresponding endoscopic relation, and let…

Let $G$ be quasisplit over $E$, fix a Whittaker datum, and assume that the connected split center of $G$ is trivial. Let $\varphi$ be an elliptic $L$-parameter, let $S_\varphi$ be…

Let $\widetilde{\pi}$ and $\widetilde{\pi}'$ be cuspidal automorphic representations of $\mathrm{GL}_n(\mathbb{A}_E)$, and let $\mathrm{L}(\widetilde{\pi})$ and…

Let $n\geq 3$, and let $\widetilde{\pi}$ be a cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_E)$. Write $\mathcal M(\mathrm{L}(\widetilde{\pi}))$ for the number o…

Let $F$ be a local field, let $G=\operatorname{GU}_n$, let $\RU_n$ be the associated unitary group, and let $\phi\in\Phi_{\mathrm{bdd}}(G)$ be a bounded Langlands parameter. Let…

Let $G$ and $G'$ be inner forms, and let $\phi$ and $\phi'$ be automorphisms arising from the corresponding adjoint groups. Suppose they correspond under the natural isomorphism of…

Let $\underline{G}$ be a connected algebraic group defined over a local field $F$, and let $\theta:\underline{G}\longrightarrow\underline{G}$ be an involution defined over $F$. Set…

Tempered $L$-packet conjecture. Every tempered $L$-packet contains a generic representation.

Let $F$ be a local field and let ${\rm U}_N(F)$ be a unitary group. A Langlands parameter is a homomorphism … A parameter is tempered when its image in ${\rm GL}_N(\mathbb{C})$ is…

Let $F$ be a non-archimedean local field, $G$ a connected reductive algebraic group over $F$, and ${\mathfrak s}=[L,\omega]_G$ an inertial equivalence class. Let $T_{\mathfrak s}$…

Let $G$ be a reductive $p$-adic group, let $Z_G$ be its Bernstein center, and let $\operatorname{Irr}(G)$ be the set of irreducible smooth representations of $G$. A stable distribu…

Let $K$ be a local function field of characteristic $2$. The standard Borel subgroup of $\mathrm{SL}_2(K)$ admits countably many ramified quadratic characters. In the associated ge…

Gross–Reeder L-packet conjecture. Each such orbit should constitute an $L$-packet, and the parameter of this $L$-packet should be a simple wild parameter.