Lie Theory and Geometry pp 569-576 | Cite as

# The Spectrum of Certain Invariant Differential Operators Associated to a Hermitian Symmetric Space

Chapter

## Abstract

Let *G/K* be an irreducible Hermitian symmetric space of rank *n* and let g = t + p _{+} + p _{−} be the usual decomposition of g = Lie(*G*). Let us write P, D, and W = P ⊗D, respectively, for the algebra of holomorphic polynomials, the algebra of constant coefficient holomorphic differential operators, and the “Weyl algebra” of polynomial coefficient holomorphic differential operators on p_{−}, and regard all three as *K*-modules in the usual way.

## Keywords

Symmetric Space Symmetric Polynomial High Weight Vector Tube Type Hermitian Symmetric Space
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## Copyright information

© Springer Science+Business Media New York 1994