Related papers: Standard modules and intertwining operators for re…

In this paper, following a similar procedure developed by Buttcane and Miller in \cite{MillerButtcane} for $SL(3,\RR)$, the $(\frakg,K)$-module structure of the minimal principal series of real reductive Lie groups $SU(2,1)$ is described…

In this paper, we study the irreducibility of $\mathcal{U}(\mathfrak{g})^{G'}$-modules on the spaces of intertwining operators in the branching problem of reductive Lie algebras, and construct a family of finite-dimensional irreducible…

In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is…

We provide results on the smoothness of normalisers in connected reductive algebraic groups $G$ over fields $k$ of positive characteristic $p$. Specifically we we give bounds on $p$ which guarantee that normalisers of subalgebras of…

Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for $G$ and the…

We give an answer to the abstract Capelli problem: Let $(G, V)$ be a multiplicity-free finite-dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

Given an elliptic curve over a field $K$ of algebraic numbers, we associate with it an action of the absolute Galois group $G_K$ in the type $A_1$ rigid DAHA-modules at roots of unity $q$ and over the rings $Z[q^{1/4}]/(p^m)$ for…

We study the parabolically induced complex representations of the unitary group in 5 variables, $ U(5), $ defined over a p-adic field. Let $ F $ be a p-adic field. Let $ E : F $ be a field extension of degree two. Let $ Gal(E : F ) = \{ 1 ,…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

Without using the $p$-adic Langlands correspondence, we prove that for many finite length smooth representations of $\mathrm{GL}_2(\mathbf{Q}_p)$ on $p$-torsion modules the $\mathrm{GL}_2(\mathbf{Q}_p)$-linear morphisms coincide with the…

On montre comment les conjectures d'Arthur permettent de calculer les points de r\'eductibilit\'e pour les induites de cuspidales des groupes classiques. Les conjectures d'Arthur utilis\'ees portent sur l'existence d'un rel\`evement faible…

Let $G$ be a group, $F$ a field, and $A$ a finite-dimensional central simple algebra over $F$ on which $G$ acts by $F$-algebra automorphisms. We study the ideals and subalgebras of $A$ which are preserved by the group action. Let $V$ be the…

In a previous work, we have shown that a representation of a $p$-adic group obtained by (normalized) parabolic induction from an irreducible supercuspidal representation $\sigma $ of a Levi subgroup $M$ contains a subquotient which is…

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the…

Let ${\bf G}$ be a simply connected semisimple algebraic group over $\Bbbk=\bar{\mathbb{F}}_q$, the algebraically closure of $\mathbb{F}_q$ (the finite field with $q=p^e$ elements), and $F$ be the standard Frobenius map. Let ${\bf B}$ be an…

Intertwining operators play an essential role and appear everywhere in the Langlands program, their analytic properties interact directly, yet deeply with the decomposition of parabolic induction locally and the residues of Eisenstein…

Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is…

Let $G$ be a complex reductive group and $H=G^{\theta}$ be its fixed point subgroup under a Galois involution $\theta$. We show that any $H$-distinguished representation $\pi$ (i.e $\mathrm{dim}_{\mathbb{C}}\left(\pi^{*}\right)^{H}\neq0$)…

Let $G$ be a (split) reductive group over $\mathbb{F}_q$, and let $M$ be a standard Levi subgroup of $G$. Consider $P$ and $P'$ parabolics in $G$, containing $M$, with Levi factor $M$. we let $U = R_u(P)$ (resp., $U' = R_u(P')$) denote the…