Homogeneous Vector Bundles and intertwining Operators for Symmetric Domains

TL;DR

This paper generalizes the properties of homogeneous Cowen-Douglas operators from the unit disk to hermitian bounded symmetric domains of any rank, expanding their theoretical framework.

Contribution

It extends the theory of homogeneous Cowen-Douglas operators to higher-rank symmetric domains, providing new insights into their structure and intertwining operators.

Findings

Generalization of Cowen-Douglas operators to symmetric domains

Characterization of intertwining operators in this setting

New structural results for homogeneous vector bundles

Abstract

The main features of homogeneous Cowen-Douglas operators, well-known for the unit disk, are generalized to the setting of hermitian bounded symmetric domains of arbitrary rank.