Geodesic
Holomorphic Multiplier Representations for Bounded Homogeneous Domains
Journal of Lie theory, Tome 30 (2020) no. 4, pp. 1091-1116
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We study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of the identity component of an algebraic group acting transitively on the domain. The classification of all such unitary representations is accomplished in this paper. As an application, we give an explicit description of the classification for a specific five-dimensional non-symmetric bounded homogeneous domain.
Classification : 32M05, 22E45
Mots-clés : Homogeneous bounded domain, Siegel domain, normal j-algebra, reproducing kernel, multiplier representation, invariant Hilbert space 
@article{JLT_2020_30_4_JLT_2020_30_4_a9,
     author = {K. Arashi},
     title = {Holomorphic {Multiplier} {Representations} for {Bounded} {Homogeneous} {Domains}},
     journal = {Journal of Lie theory},
     pages = {1091--1116},
     year = {2020},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_4_JLT_2020_30_4_a9/}
}
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K. Arashi. Holomorphic Multiplier Representations for Bounded Homogeneous Domains. Journal of Lie theory, Tome 30 (2020) no. 4, pp. 1091-1116. http://geodesic.mathdoc.fr/item/JLT_2020_30_4_JLT_2020_30_4_a9/