Unitarizable Vector-Valued Holomorphic Discrete Series and the Laplace Transform : an Example

摘要

For T-Omega a Hermitian symmetric tube-type domain, a family (pi(mu)) (mu epsilon C) of holomorphic vector-valued representations is studied. The corresponding Wallach set is determined. The main tool is a realization of the representations as weighted L-2 -spaces on the cone Omega through the Laplace transform.