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

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 $π_ν$ of $G$ for $ν$ in an interval on $\mathbb R^+$, the so-called complementary series, and subquotient or subrepresentations of $G$ for $ν$ being negative integers. We consider the restriction of $(π_ν, G)$ 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.