Finite-dimensional representations of invariant differential operators
type: Item
instance of: scholarly article
title: Finite-dimensional representations of invariant differential operators
zbMATH Open document ID: 1020.22005
DOI: 10.1016/S0021-8693(02)00500-8
author: Gerald W. Schwarz
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: Let \(G\) be a reductive complex algebraic group and \(V\) a finite-dimensional \(G\)-module. Denote by \(\mathcal{B}=\left( \mathcal{D}(V)\right) ^{G}\) the algebra of \(G\)-invariant algebraic differential operators on \(V\). For \(G=SL_{3}(\mathbb{R)}\) and its adjoint representation, the author studies finite-dimensional representations of \(\mathcal{B}\) and primitive ideals of \(\mathcal{B}\).
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1868084
zbMATH Keywords: invariant differential operators
zbMATH Keywords: representations
reviewed by: Guy Roos
MaRDI profile type: Publication
cites work: Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
cites work: Q4065692
cites work: Q4392287
cites work: Differential Operators on a Semisimple Lie Algebra
cites work: Invariant Differential Operators and Distributions on a Semisimple Lie Algebra
cites work: Moduln mit einem höchsten Gewicht
cites work: Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules
cites work: Structure of representations with highest weight of infinite-dimensional Lie algebras
cites work: A Harish-Chandra homomorphism for reductive group actions
cites work: The asymptotic behavior of invariant collective motion
cites work: Invariant algebras and completely reducible representations
cites work: Hereditary properties of direct summands of algebras
cites work: Invariant Differential Operators and an Homomorphism of Harish-Chandra
cites work: The kernel of an homomorphism of Harish-Chandra
cites work: Fixed rings of finite automorphism groups of associative rings
cites work: Invariants under tori of rings of differential operators and related topics
cites work: Lifting differential operators from orbit spaces
cites work: Q4338612
cites work: On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
cites work: The ring of invariants of matrices
cites work: Some rings of differential operators for \(\text{Sl}_ 2\)-invariants are simple
description: scientific article; zbMATH DE number 1868084