New constructions of homogeneous operators

Abstract

New examples of homogeneous operators involving infinitely many parameters are constructed. They are realized on Hilbert spaces of holomorphic functions with reproducing kernels which are computed explicitly. All the examples are irreducible and belong to the Cowen–Douglas class. Even though the construction is completely explicit, it is based on certain facts about Hermitian holomorphic homogeneous vector bundles. These facts also make possible a description of all homogeneous Cowen–Douglas operators, in a somewhat less explicit way. To cite this article: A. Korányi, G. Misra, C. R. Acad. Sci. Paris, Ser. I 342 (2006).