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Tensor products of complementary series of rank one Lie groups

Genkai Zhang (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori)
Science China - Mathematics (1674-7283). Vol. 60 (2017), 11, p. 2337-2348.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: semisimple Lie groups, unitary representations, tensor products, complementary series, intertwining operators



Denna post skapades 2017-11-08.
CPL Pubid: 253018

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)

Ämnesområden

Matematik

Chalmers infrastruktur