Geodesic
Norm Computation and Analytic Continuation of Vector Valued Holomorphic Discrete Series Representations
Journal of Lie theory, Tome 26 (2016) no. 4, pp. 927-99
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We compute explicitly the norm of the vector-valued holomorphic discrete series representations, when its K-type is "almost multiplicity-free". As an application, we discuss the properties of highest weight modules, such as unitarizability, reducibility and composition series.
Classification : 22E45, 43A85, 17C30
Mots-clés : Holomorphic discrete series representations, highest weight modules, Jordan triple systems, composition series 
@article{JLT_2016_26_4_JLT_2016_26_4_a1,
     author = {R. Nakahama},
     title = {Norm {Computation} and {Analytic} {Continuation} of {Vector} {Valued} {Holomorphic} {Discrete} {Series} {Representations}},
     journal = {Journal of Lie theory},
     pages = {927--99},
     year = {2016},
     volume = {26},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a1/}
}
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R. Nakahama. Norm Computation and Analytic Continuation of Vector Valued Holomorphic Discrete Series Representations. Journal of Lie theory, Tome 26 (2016) no. 4, pp. 927-99. http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a1/