相关论文: Equivariant D-modules

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…

We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…

Let X be an algebraic curve. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined (aka rational) maps from X to a fixed target scheme Y. There are three…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

In this paper we address several algebraic constructions in the context of groupoids, algebroids and $\mathbb Z$-graded manifolds. We generalize the results of integration of $\mathbb N$-graded Lie algebras to the honest $\mathbb Z$-graded…

This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…

This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

We introduce stacks classifying \'etale germs of pointed n-dimensional varieties. We show that quasi-coherent sheaves on these stacks are universal D- and O-modules. We state and prove a relative version of Artin's approximation theorem,…

Using a representation theoretic parameterization for the orbits in the enhanced cyclic nilpotent cone, derived by the authors in a previous article, we compute the fundamental group of these orbits. This computation has several…

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…

The effectiveness of the aplication of constructions in $G$-graded $k$-categories to the computation of the fundamental group of a finite dimensional $k$-algebra, alongside with open problems still left untouched by those methods and new…

We study the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme G((t))/I, where I is the Iwahori subgroup. We prove a…

The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Z^d-graded binomial ideal I along with Euler operators defined by the grading and a parameter in C^d. We determine the parameters for which these…

We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.

We classify groups G such that the unit group U(ZG) is hypercentral. In the second part we classify groups G whose modular group algebra has hyperbolic unit group V(KG).

This paper investigates structure of Banach convolution modules induced by group algebras on covariant functions of characters of closed normal subgroups. Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a…