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Transactions of the American Mathematical Society

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Composition series for analytic continuations of holomorphic discrete series representations of $ {\rm SU}(n,\,n)$


Author: Bent Ørsted
Journal: Trans. Amer. Math. Soc. 260 (1980), 563-573
MSC: Primary 22E45; Secondary 05A10, 43A85, 81C40
MathSciNet review: 574799
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Abstract: We study a certain family of holomorphic discrete series representations of the semisimple Lie group $ G\, = \,SU(n,\,n)$ and the corresponding analytic continuation in the inducing parameter $ \lambda $. At the values of $ \lambda $ where the representations become reducible, we compute the composition series in terms of a Peter-Weyl basis on the Shilov boundary of the Hermitian symmetric space for G.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0574799-X
Keywords: Representations of Lie groups, holomorphic discrete series, harmonic analysis, composition series, Shilov boundary, generalized binomial formula
Article copyright: © Copyright 1980 American Mathematical Society