Tensor products of complementary series of rank one Lie groups

We consider the tensor product πα ⊗ πβ of 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+β for 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 ⊗ πβ of two complementary series πα and πβ where k = k(α, β n) depends on α, β and n.