Tensor products of analytic continuations of holomorphic discrete series 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 theoremCategories:22E45, 43A85, 32M15, 33A65