Differential Operators on Equivariant Vector Bundles Over Symmetric Spaces
Date
2000-09-01
Authors
Deitmar, Anton
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger algebra of all invariant operators. We compute the possible eigencharacters and show that for invariant integral operators the eigencharacter is given by the Abel transform. We show that sufficiently regular operators are surjective, i.e. that equations of the form <i>D</i> ƒ = u are solvable for all u.
Description
Keywords
Invariant operators
Citation
Deitmar, A. (2000). Differential operators on equivariant vector bundles over symmetric spaces. <i>Electronic Journal of Differential Equations, 2000</i>(59), pp. 1-8.
Rights
Attribution 4.0 International