Tensor products of complementary series of rank one Lie groups

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（11）
• 页码范围: 2337-2348
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11425-017-9149-4

摘要

We consider the tensor product πα (×) πβ of complementary series representations πα and πβ of classical rank one groups SOo(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 SOo(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.