Vector-valued holomorphic discrete series and the Laplace transform : an example

For T $Ω$ a Hermitian symmetric tube-type domain, a family ($π$ $μ$) $μ$$\in$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 $Ω$ through the Laplace transform.

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