Discrete components in restriction of unitary representations of rank one semisimple Lie groups

Abstract

We consider spherical principal series representations of the semisimple Lie group of rank one $G=SO(n,1;\mathbb{K})$, $\mathbb K=\br, \bc, \bh$. There is a family of unitarizable representations ${\pi }_{\nu }$ of $G$ for $\nu$ in an interval on ${\mathbb{R}}^{+}$, the so-called complementary series, and subquotient or subrepresentations of $G$ for $\nu$ being negative integers. We consider the restriction of $({\pi }_{\nu },G)$ under the subgroup $H=SO(n-1,1;\mathbb{K})$. We prove the appearing of discrete components. The corresponding results for the exceptional Lie group $F_{4(-20)}$ and its subgroup $Spin(8,1)$ are also obtained.

Revised version

References in corpus (1)

• Quelques conséquences des travaux d'Arthur pour le spectre et la topologie des variétés hyperboliques

Cited by in corpus (2)

• Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups
• Restriction of some unitary representations of O(1,N) to symmetric subgroups