Geodesic
Unitarizable Vector-Valued Holomorphic Discrete Series and the Laplace Transform: an Example
Journal of Lie Theory, Tome 33 (2023) no. 1, pp. 133-148

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For $T_\Omega$ a Hermitian symmetric tube-type domain, a family $(\pi_\mu)_{\mu\in \mathbb{C}}$ 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.
Classification : 22E46, 32M15, 44A10
Mots-clés : Tube-type domains, Euclidean Jordan algebras, holomorphic discrete series, weighted Bergman spaces, Laplace transform, Wallach set 
J.-L. Clerc. Unitarizable Vector-Valued Holomorphic Discrete Series and the Laplace Transform: an Example. Journal of Lie Theory, Tome 33 (2023) no. 1, pp. 133-148. http://geodesic.mathdoc.fr/item/JOLT_2023_33_1_a5/
@article{JOLT_2023_33_1_a5,
     author = {J.-L. Clerc},
     title = {Unitarizable {Vector-Valued} {Holomorphic} {Discrete} {Series} and the {Laplace} {Transform:} an {Example}},
     journal = {Journal of Lie Theory},
     pages = {133--148},
     year = {2023},
     volume = {33},
     number = {1},
     zbl = {1540.22028},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_1_a5/}
}
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