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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 1, Pages 34–53 (Mi izv1792)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:1, 31–50

Bibliographic databases:

UDC: 513.88
MSC: Primary 20G05; Secondary 20G20, 22E30, 22E45
Received: 25.11.1975

Citation: 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., 41:1 (1977), 34–53; Math. USSR-Izv., 11:1 (1977), 31–50

Citation in format AMSBIB
\Bibitem{Zhe77}
\by D.~P.~Zhelobenko
\paper A~description of the quasi-simple irreducible representations of the groups $U(n,1)$ and $\operatorname{Spin}(n,1)$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 1
\pages 34--53
\mathnet{http://mi.mathnet.ru/izv1792}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=450464}
\zmath{https://zbmath.org/?q=an:0356.22013|0381.22003}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 31--50
\crossref{https://doi.org/10.1070/IM1977v011n01ABEH001692}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Khoroshkin, “Category of Harish-Chandra modules of the group $SU(n,1)$”, Funct. Anal. Appl., 14:2 (1980), 153–155  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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