Electron. J. Diff. Eqns., Vol. 2000(2000), No. 59, pp. 1-8.

Differential operators on equivariant vector bundles over symmetric spaces

Anton Deitmar

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 $Df=u$ are solvable for all $u$.

An addendum to this article was attached on February 26, 2001. In this addendum, the original proof of Theorem 4.4 is expanded.

Submitted May 16, 2000. Published September 1, 2000.
Math Subject Classifications: 43A85, 22E30, 35J45.
Key Words: invariant operators.

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Anton Deitmar
School of Mathematical Sciences
University of Exeter
Laver Building, North Park Road
Exeter, EX4 4QE
Devon, UK
email: A.H.J.Deitmar@exeter.ac.uk

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