Discrete components in restriction of unitary representations of rank one semisimple Lie groups
Journal article, 2015

We consider spherical principal series representations of the semisimple Lie group of rank one G=SO(n,1;K)G=SO(n,1;K), K=R,C,HK=R,C,H. There is a family of unitarizable representations πνπν of G for ν in an interval on RR, the so-called complementary series, and subquotients or subrepresentations of G for ν being negative integers. We consider the restriction of (πν,G)(πν,G) under the subgroup H=SO(n−1,1;K)H=SO(n−1,1;K). We prove the appearing of discrete components. The corresponding results for the exceptional Lie group F4(−20)F4(−20) and its subgroup Spin0(8,1)Spin0(8,1) are also obtained.

Author

Genkai Zhang

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 269 12 3689-3713

Subject Categories

Geometry

Mathematical Analysis

DOI

10.1016/j.jfa.2015.09.021

More information

Created

10/7/2017