RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1767 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

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} 

• http://mi.mathnet.ru/eng/izv1792
• http://mi.mathnet.ru/eng/izv/v41/i1/p34

 SHARE:

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
•  Number of views: This page: 138 Full text: 55 References: 25 First page: 1