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We consider spherical principal series representations of the semisimple Liegroup of rank one $G=SO(n, 1; \mathbb K)$, $\mathbb K=\br, \bc, \bh$. There isa family of unitarizable representations $\pi_{\nu}$ of $G$ for $\nu$ in aninterval on $\mathbb R^+$, the so-called complementary series, and subquotientor subrepresentations of $G$ for $\nu$ being negative integers. We consider therestriction of $(\pi_{\nu}, G)$ under the subgroup $H=SO(n-1, 1; \mathbb K)$.We prove the appearing of discrete components. The corresponding results forthe exceptional Lie group $F_{4(-20)}$ and its subgroup $Spin(8,1)$ are alsoobtained.

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