33 problems

Aubert–Moussaoui–Solleveld conjecture on supercuspidal enhanced L-parameters
arXiv@arxiv
Let $G$ be a quasi-split reductive group over a non-Archimedean local field $F$ , let $G'$ be an inner form, and let enhanced L-parameters for $G'$ be defined as pairs…
Conjectureopenlocal-langlands-correspondence p-adic-groups supercuspidal-representations
0
Cuspidal local Langlands correspondence conjecture
arXiv@arxiv
Cuspidal LLC conjecture. Under the local Langlands correspondence, $\Phi_{\mathrm{cusp}}(G)$ corresponds to the set of supercuspidal irreducible smooth $G$ -representations. This pr…
Conjectureopenlocal-langlands-correspondence representation-theory supercuspidal-representations
0
The folklore conjecture on compact induction of supercuspidal representations
arXiv@arxiv
Let $G$ be the $p$ -adic classical group considered in the paper, and let $\pi$ be an irreducible supercuspidal representation of $G$ . A representation is compactly induced if it is…
Conjectureopenclassical-groups p-adic-representations supercuspidal-representations
0
The conjecture on geometrically minimal K-types
arXiv@arxiv
Let $(\pi,V)$ be an irreducible supercuspidal representation of $G$ , and let ${\mathscr{S}}$ be the $G$ -equivariant Schneider–Stuhler sheaf on the building $X$ associated with…
Conjectureopenp-adic-representations supercuspidal-representations types
1
The compact induction conjecture for supercuspidal representations
arXiv@arxiv
Let $F$ be a nonarchimedean local field, let $\boldsymbol{\mathrm{G}}$ be a connected reductive group defined over $F$ , and let $G=\boldsymbol{\mathrm{G}}(F)$ with center $Z$ . Let…
Conjectureopencompact-induction p-adic-representations supercuspidal-representations
0
The compact-induction conjecture for supercuspidal representations of p-adic groups
arXiv@arxiv
Let $F$ be a non-archimedean local field and let $G$ be a connected reductive group over $F$ . A compact-mod-center open subgroup of $G(F)$ is an open subgroup whose image in the qu…
Conjectureopenp-adic-groups representation-theory supercuspidal-representations
0
Refined leading-term conjecture for regular supercuspidal connections
arXiv@arxiv
Let $G_1,\ldots,G_p$ be twisted Levi subgroups, let $\phi_{(i)}:\fa_i\to\bC$ be refined leading terms, let $X_{(i)}\in\check{\fa}_i$ be their duals, and let $A'$ and the central su…
Conjecturesolvedformal-connections geometric-langlands supercuspidal-representations
0
Explicit local Langlands conjecture for toral supercuspidal representations
arXiv@arxiv
Let $G$ be a connected simple algebraic group, let $\hg$ be the associated affine Kac–Moody algebra at critical level, and let $(J,\tphi)$ be a $K$ -type for the loop group obtained…
Conjecturesolvedformal-connections geometric-langlands supercuspidal-representations
0
Supercuspidal wavefront-set conjecture
arXiv@arxiv
Supercuspidal wavefront-set conjecture. One has
Conjectureopenp-adic-groups supercuspidal-representations wavefront-sets
0
The folklore conjecture on generic supercuspidals and discrete Langlands parameters
arXiv@arxiv
Folklore conjecture. Generic supercuspidal representations should correspond under the local Langlands correspondence to $\mathrm{SL}_2$ -trivial discrete parameters.
Conjectureopenlocal-langlands-correspondence p-adic-groups supercuspidal-representations
0
Cuspidality criterion in the refined local Langlands correspondence
arXiv@arxiv
Fix a reductive group $G$ , a rigid inner twist, a Whittaker datum $\mathfrak w$ , and the refined local Langlands reciprocity map $\operatorname{rec}_{\mathfrak w}$ . An enhanced $L$ …
Conjectureopenlocal-langlands supercuspidal-representations
0
The local Langlands correspondence for connected reductive groups
arXiv@arxiv
The local Langlands correspondence. The set $\Pi(\mathbf{G})$ is partitioned into the disjoint union of finite sets
Conjectureopenlocal-langlands-correspondence representation-theory supercuspidal-representations
0
The conjecture on cyclic base change eliminating supercuspidal representations
arXiv@arxiv
Let $F_0$ be a local field, let $G$ be a reductive group over $F_0$ , let $\pi_0\in\Pi(G/F_0)$ be any supercuspidal representation, and let $\Pi_0\subset\Pi(G/F_0)$ be the packet co…
Conjecturesolvedbase-change local-langlands supercuspidal-representations
0
The conjecture on pure incorrigible supercuspidal representations
arXiv@arxiv
Let $F$ be a local field, let $G$ be a reductive group over $F$ , and call a supercuspidal representation pure incorrigible when it is pure and remains supercuspidal in the base-cha…
Conjecturesolvedbase-change local-langlands supercuspidal-representations
0
The compact-modulo-center induction conjecture for supercuspidal representations
arXiv@arxiv
Compact-modulo-center induction conjecture. Every supercuspidal representation of a $p$ -adic group is isomorphic to the compact induction of some finite-dimensional irreducible rep…
Conjecturesolvedcompact-induction p-adic-groups supercuspidal-representations
1
Categorical local Langlands conjecture for elliptic parameters
arXiv@arxiv
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…
Conjectureopenlocal-langlands l-packets supercuspidal-representations
0
Yu's conjecture that the Hecke algebras of his types are mutually isomorphic
arXiv@arxiv
Let $G$ be a connected reductive group over a non-archimedean local field $F$ . Suppose Yu's construction starts with a tuple…
Conjectureopenhecke-algebras p-adic-groups supercuspidal-representations
1
Yu's conjecture on Hecke algebras of tame supercuspidal types
arXiv@arxiv
Let $F$ be a non-archimedean local field of residue characteristic $p\neq 2$ , let $G$ be a connected reductive group over $F$ that splits over a tamely ramified extension, and let…
Conjectureopenhecke-algebras p-adic-groups supercuspidal-representations
1
Exterior-square local converse conjecture for unitarizable supercuspidal representations
arXiv@arxiv
Let $F$ be a local non-Archimedean field, let $n$ be a positive integer, and let $\pi_1$ and $\pi_2$ be irreducible unitarizable supercuspidal representations of…
Conjectureopengamma-factors local-converse-theorems supercuspidal-representations
0
The stable character formula for supercuspidal Langlands parameters
arXiv@arxiv
Let $F$ be a non-archimedean local field, let $G$ be a reductive group that splits over a tame extension of $F$ , and assume that the residue characteristic is sufficiently large fo…
Conjectureopenendoscopy local-langlands-correspondence supercuspidal-representations
0
Supercuspidality criterion for unitary-group L-packets
arXiv@arxiv
Unitary-group supercuspidality conjecture. The packet $\Pi_{\phi}$ consists of supercuspidal representations if and only if $\phi$ is discrete and its restriction to…
Conjectureopenlocal-langlands supercuspidal-representations unitary-groups
0
The compact induction conjecture for irreducible supercuspidal representations
arXiv@arxiv
Let $G$ be a reductive group and let $\mathcal{M}(G)$ denote the representations of $G$ . Let $\pi\in\mathcal{M}(G)$ be irreducible and supercuspidal. A subgroup $K$ of $G$ is compa…
Conjectureopenp-adic-groups representation-theory supercuspidal-representations
0
KST character-decay conjecture for supercuspidal representations
arXiv@arxiv
KST character-decay conjecture. The following assertions hold:
Conjectureopenp-adic-groups representation-theory supercuspidal-representations
0
The unicity of types conjecture for supercuspidal representations
arXiv@arxiv
Let $G=\mathbf{G}(F)$ be the group of rational points of a connected reductive algebraic group over a non-archimedean local field, and let $\pi$ be a supercuspidal representation o…
Conjectureopenp-adic-groups representation-theory supercuspidal-representations
0
The field-of-rationality lower-bound conjecture for positive-depth supercuspidals
arXiv@arxiv
Let $G/F$ be a connected reductive group, and let $|W|$ be the cardinality of the Weyl group of a maximal torus in $G\times\overline{F}$ . Let $\mathfrak{p}$ be a prime such that…
Conjectureopenautomorphic-representations fields-of-rationality supercuspidal-representations
0