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 Holomorphic discrete series, tensor product, spherical function, Clebsch-Gordan coefficient, Plancherel theorem

MSC Classifications:

22E45, 43A85, 32M15, 33A65 show english descriptions Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
Analysis on homogeneous spaces
Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
unknown classification 33A65 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

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