Weighted Bergman inner products on subspaces of bounded symmetric domains (Developments in Representation Theory and Related Topics)

Abstract

Let Hr(F) (F=R, C, H) be the space of Hermitian matrices, and we consider the bounded symmetric domain D⊂Hr(F)C. In this article we present a result on the computation of the weighted Bergman inner product on D of a polynomial on the subspace Hr', (F)⊕Hr"(F) and an exponential function on Hr(F). Also, as an application, we present a result on explicit construction of intertwining operators from representations of Sp(r, R)to those of the subgroup U(r', r").