Representations of complementary series entering descretely in tensor products of unitary representations (Q1085286)

The author considers the problem of decomposing the tensor product of two unitary representations of a semi-simple Lie group G which belong to complementary series induced from a maximal parabolic subgroup. Such decomposition is shown for \(G=SO_ 0(p,1)\) for the spherical complementary series (and analogously for \(G=U(p,1)\), Sp(p,1)). It is claimed that the analogous facts take place for \(G=SO_ 0(p,q)\), U(p,q), Sp(p,q). It is pointed out that arguments may be transferred onto the indefinite complementary series. Moreover Stein representations of \(G=SL(2n, {\mathbb{R}})\), SL(2n, \({\mathbb{C}})\) and representations of \(SO_ 0(p,q)\) associated with the cone are also considered.