D. P. Zhelobenko, “A description of the quasi-simple irreducible representations of the groups $U(n,1)$ and $\operatorname{Spin}(n,1)$”, Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 1,Pages 34

This article is cited in 2 papers

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

D. P. Zhelobenko

Abstract: 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 $E(\sigma)$.
Bibliography: 9 titles.

UDC: 513.88

MSC: Primary 20G05; Secondary 20G20, 22E30, 22E45

Received: 25.11.1975