Holomorphic multiplier representations for bounded homogeneous domains

TL;DR

This paper classifies all unitary representations derived from holomorphic sections of line bundles over bounded homogeneous domains, providing a comprehensive understanding of their structure and applications to specific domains.

Contribution

It offers a complete classification of holomorphic multiplier representations for bounded homogeneous domains, including explicit results for a five-dimensional non-symmetric case.

Findings

Complete classification of unitary representations on bounded homogeneous domains

Explicit classification for a five-dimensional non-symmetric domain

Framework for unitarizations in holomorphic line bundle spaces

Abstract

In this paper, we study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of a connected algebraic group acting transitively on the domain. We give a complete classification of unitary representations arising from such unitarizations. As an application, we classify all such unitary representations for a specific five-dimensional non-symmetric bounded homogeneous domain.