Tensor products of complementary series of rank one Lie groups
Artikel i vetenskaplig tidskrift, 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.

semisimple Lie groups

complementary series

tensor products

intertwining operators

unitary representations

Författare

Genkai Zhang

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Science China Mathematics

1674-7283 (ISSN)

Vol. 60 11 2337-2348

Ämneskategorier

Matematik

DOI

10.1007/s11425-017-9149-4

Mer information

Skapat

2017-11-08