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Journal of Lie Theory 30 (2020), No. 4, 1091--1116
Copyright Heldermann Verlag 2020

Holomorphic Multiplier Representations for Bounded Homogeneous Domains

Koichi Arashi
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

We study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of the identity component of an algebraic group acting transitively on the domain. The classification of all such unitary representations is accomplished in this paper. As an application, we give an explicit description of the classification for a specific five-dimensional non-symmetric bounded homogeneous domain.

Keywords: Homogeneous bounded domain, Siegel domain, normal j-algebra, reproducing kernel, multiplier representation, invariant Hilbert space.

MSC: 32M05, 22E45.

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