Unitary holomorphic multiplier representations over a homogeneous bounded domain

Abstract

We consider the unitarizability of multiplier representations of transformation groups defined on Hilbert spaces of holomorphic functions on a homogeneous bounded domain. In particular, for the Iwasawa subgroup of the holomorphic automorphism group the classification of the unitary multiplier representations is accomplished by making use of results in [Ishi, J. Funct. Anal. 167: 425–462, 1999]. As an application, the Wallach set of the homogeneous bounded domain is described.