Related papers: Parabolic induction and the Harish-Chandra D-modul…

Let $LG_n$ denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension $2n.$ For each strict partition $\lambda=(\lambda_1,...,\lambda_k)$ with $\lambda_1\leq n$…

In a recent paper Ben-Zvi and Nadler proved that the induction map from $B$-bundles of degree 0 to semistable $G$-bundles of degree 0 over an elliptic curve is a small map with Galois group isomorphic to the Weyl group of $G$. We generalize…

This paper is the continuation of \cite{CXY}. 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…

For $\mathbb{G}$ an algebraic (or more generally, a bornological) quantum group and $\mathbb{B}$ a closed quantum subgroup of $\mathbb{G}$, we build in this paper an induction module by explicitly defining an inner product which takes its…

Let $G$ be a groupoid acting on a set $X$ and let $R$ be a $G$-graded ring with graded local units. We study the main properties of the category $gr-(R,G,X)$ of $X$-graded $R$-modules and adjoint functors between categories of this kind. We…

Let $Bun_G(X)$ be the moduli stack of $G$-torsors on a smooth projective curve $X$ for a reductive group $G$. We prove a conjecture made by Drinfeld-Wang and Gaitsgory on the Deligne-Lusztig duality for D-modules on $Bun_G(X)$. This…

Given a regular supercuspidal representation $\rho$ of the Levi subgroup $M$ of a standard parabolic subgroup $P=MN$ in a connected reductive group $G$ defined over a non-archimedean local field $F$, we serve you a Rodier type structure…

A famous theorem of Harish-Chandra shows that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We give here an algebraic version of this theorem in terms of polynomials associated with a holonomic…

Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…

Let $A$ be an Artinian local ring with algebraically closed residue field $k$, and let $\mathbf{G}$ be an affine smooth group scheme over $A$. The Greenberg functor $\mathcal{F}$ associates to $\mathbf{G}$ a linear algebraic group…

The aim of the present paper is to study arithmetic properties of $\mathcal{D}$-modules on an algebraic variety over the field of algebraic numbers. We first provide a framework for extending a class of $G$-connections (resp., globally…

Let $G$ be a group that is relatively hyperbolic with respect to a collection of subgroups $\{H_{\lambda}\}_{\lambda\in \Lambda}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ with respect to this collection. We…

In this paper, we classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higher-dimensional analogue of the affine-Virasoro algebra. In particular, we complete the classification of…

Let $G_R$ be a classical real direct limit Lie group and $g_R$ its Lie algebra. The parabolic subalgebras of the complexification $g_C$ were described by the first two authors. In the present paper we extend these results to $g_R$. This…

Let $H$ be an infinite-dimensional complex Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian formed by closed subspaces of $H$ whose dimension and codimension both are infinite. We say that $X,Y\in {\mathcal…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

In this paper, we shall establish the Mackey formulas in the following two set ups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of…

We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a…

In this article a class of additive invariant positive selfadjoint pseudodifferential unbounded operators on $L^{2}(\mathbb{A}_{f})$, where $\mathbb{A}_{f}$ is the ring of finite ad\'eles of the rational numbers, is considered to state a…

Let $G_n$ be an inner form of a general linear group over a non-Archimedean field. We fix an arbitrary irreducible representation $\sigma$ of $G_n$. Lapid-M\'inguez give a combinatorial criteria for the irreducibility of parabolic induction…