A description of the quasi-simple irreducible representations of the groups $U(n,1)$ and $\operatorname{Spin}(n,1)$

This article deals with a family of elementary $G$-modules $E(\sigma)$, where $G$ is either one of the groups $U(n,1)$, with $n>1$, or one of the groups $\operatorname{Spin}(n,1)$, wit $n>2$. A description is given of all of the submodules of $E(\sigma)$; in addition, these submodules are characterized in terms of the kernels and images of the intertwining operators (symmetry operators). A description is given of all of the factors of $E(\sigma)$ up to isomorphism. It follows from these results that every quasi-simple irreducible Banach $G$-module is infinitesimally equivalent to a submodule of some $E(\sigma)$.
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