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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 3, Pages 573–599 (Mi izv2023)  

This article is cited in 1 scientific paper (total in 2 paper)

Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups

D. P. Zhelobenko


Abstract: A new concept of “extremal irreducibility” for representations of Lie groups in separable locally convex spaces is introduced. All extremally irreducible representations of semisimple complex Lie groups are classified to within equivalence, i.e. to within topological isomorphism rearranging representation operators. Analogous results are obtained for other variants of axiomatics (normal irreducibility, Gel'fand irreducibility, complete irreducibility).

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:3, 589–613

Bibliographic databases:

UDC: 513.88
MSC: Primary 22E45; Secondary 43A80
Received: 10.02.1970

Citation: D. P. Zhelobenko, “Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups”, Izv. Akad. Nauk SSSR Ser. Mat., 35:3 (1971), 573–599; Math. USSR-Izv., 5:3 (1971), 589–613

Citation in format AMSBIB
\Bibitem{Zhe71}
\by D.~P.~Zhelobenko
\paper Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 3
\pages 573--599
\mathnet{http://mi.mathnet.ru/izv2023}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=289723}
\zmath{https://zbmath.org/?q=an:0238.22011}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 3
\pages 589--613
\crossref{https://doi.org/10.1070/IM1971v005n03ABEH001080}


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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. D. P. Zhelobenko, “Cyclic modules for a complex semisimple Lie group”, Math. USSR-Izv., 7:3 (1973), 497–510  mathnet  crossref  mathscinet  zmath
    2. Yu. A. Neretin, S. M. Khoroshkin, “Mathematical works of D. P. Zhelobenko”, Russian Math. Surveys, 64:1 (2009), 187–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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