Norm Computation and Analytic Continuation of Vector Valued Holomorphic Discrete Series Representations

R. Nakahama

doi:10.5802/jolt.919

R. Nakahama

Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 927-990

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.919

Classification: 22E45, 43A85, 17C30
Keywords: Holomorphic discrete series representations, highest weight modules, Jordan triple systems, composition series

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     author = {R. Nakahama},
     title = {Norm {Computation} and {Analytic} {Continuation} of {Vector} {Valued} {Holomorphic} {Discrete} {Series} {Representations}},
     journal = {Journal of Lie Theory},
     pages = {927--990},
     year = {2016},
     volume = {26},
     number = {4},
     doi = {10.5802/jolt.919},
     zbl = {1359.22011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.919/}
}

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R. Nakahama. Norm Computation and Analytic Continuation of Vector Valued Holomorphic Discrete Series Representations. Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 927-990. doi: 10.5802/jolt.919

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