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

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.