Conformally invariant systems of differential operators
type: Item
instance of: scholarly article
title: Conformally invariant systems of differential operators
zbMATH Open document ID: 1163.22007
author: Anthony C. Kable
author: R. Zierau
author: L. Barchini
published in: Advances in Mathematics
publication date: 2009-05-19T00:00:00Z
review text: The authors study the Lie algebra of first order differential operators on a manifold \(M\) and systems of (arbitrary) differential operators on \(M\) conformally invariant with respect to this Lie algebra. They establish a close connection between the existence of conformally invariant systems of differential operators and the existence of homomorphisms between certain generalized Verma modules (the latter being realized as certain spaces of distributions). As a corollary the authors obtain some results on the nonexistence of certain conformally invariant systems of third-order operators.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 5555309
zbMATH Keywords: Lie algebra
zbMATH Keywords: generalized Verma module
zbMATH Keywords: intertwining operator
zbMATH Keywords: double coset
zbMATH Keywords: flag manifold
MaRDI profile type: Publication
full work available at URL: j.aim.2009.01.006
OpenAlex ID: W2058690558
cites work: Conformally invariant systems of differential equations and prehomogeneous vector spaces of Heisenberg parabolic type
cites work: A duality theorem for extensions of induced highest weight modules
cites work: Differential operators and highest weight representations
cites work: Q4204420
cites work: Intertwining differential operators and reducibility of generalized Verma modules
cites work: Q4149922
DOI: 10.1016/J.AIM.2009.01.006
description: scientific article; zbMATH DE number 5555309