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# Tensor products of analytic continuations of holomorphic discrete series

Published:1997-12-01
Printed: Dec 1997
• Bent Ørsted
• Genkai Zhang
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## Abstract

We give the irreducible decomposition of the tensor product of an analytic continuation of the holomorphic discrete series of $\SU(2, 2)$ with its conjugate.
 Keywords: Holomorphic discrete series, tensor product, spherical function, Clebsch-Gordan coefficient, Plancherel theorem
 MSC Classifications: 22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 43A85 - Analysis on homogeneous spaces 32M15 - Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 33A65 - unknown classification 33A65