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

2022/06/15 by Clerc, Jean-Louis
#2020 MSC. Primary 22E46 #44A10 #FOS: Mathematics #Representation Theory (math.RT) #Secondary 32M15

paper · doi:10.48550/arxiv.2206.07407

Abstract

For T Ω a Hermitian symmetric tube-type domain, a family (π μ) μ∈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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• Tube domains and restrictions of minimal representations
• Integral Representations in Weighted Bergman Spaces on the Tube Domains
• The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula II. Non-tube type groups
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