Journal article, 2017

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

unitary representations

tensor products

complementary series

semisimple Lie groups

intertwining operators

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

1674-7283 (ISSN)

Vol. 60 11 2337-2348Mathematics

10.1007/s11425-017-9149-4