A Classification of Homogeneous Operators in the Cowen-Douglas Class

Abstract

A complete list of homogeneous operators in the Cowen-Douglas class $$B_n({\mathbb{D}})$$ is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.