Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 483–496 | Cite as

Unitary representations of unimodular Lie groups in Bergman spaces

Article

Abstract

For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. These representation spaces are infinite-dimensional and have compact kernels. In particular, the Bergman spaces of these natural manifolds are infinite-dimensional.

Mathematics Subject Classification (2000)

Primary 43A65 32W05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität WienViennaAustria

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