Tensor products of complementary series of rank one Lie groups

We consider the tensor product πα ? πβof complementary series representations πα and πβ of classical rank one groups SO0（n, 1）, SU（n, 1） and Sp（n, 1）. We prove that there is a discrete component πα+βfor small parameters α and β（in our parametrization）. We prove further that for SO0（n, 1） there are finitely many complementary series of the form πα+β+2j,j = 0, 1,..., k, appearing in the tensor product πα ? πβof two complementary series πα and πβ, where k = k（α, β, n） depends on α, β and n.