Tensor products of complementary series of rank one Lie groups

We consider the tensor product π_α ? π_β of complementary series representations π_α and π_β of classical rank one groups SO ₀(n; 1), SU(n; 1) and Sp(n; 1). We prove that there is a discrete component π_α+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 π_α+β+2j , j = 0, 1,..., k, appearing in the tensor product π_α ? π_β of two complementary series π_α and π_β where k = k(α, β n) depends on α, β and n.