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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 3, Pages 502–515 (Mi izv2276)  

Cyclic modules for a complex semisimple Lie group

D. P. Zhelobenko


Abstract: We consider cyclic modules generated by elementary representations of a complex semisimple Lie group. The main result is a theorem on cyclicity (Theorem 3 of § 4), according to which the elementary representations are generated by cyclic vectors of a special type with respect to a maximal compact subgroup. We give a classification of completely irreducible representations in terms of the characteristic (highest and lowest) weights.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:3, 497–510

Bibliographic databases:

UDC: 513.88
MSC: Primary 22E45, 22E60; Secondary 17B10
Received: 09.10.1972

Citation: D. P. Zhelobenko, “Cyclic modules for a complex semisimple Lie group”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973), 502–515; Math. USSR-Izv., 7:3 (1973), 497–510

Citation in format AMSBIB
\Bibitem{Zhe73}
\by D.~P.~Zhelobenko
\paper Cyclic modules for a~complex semisimple Lie group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 3
\pages 502--515
\mathnet{http://mi.mathnet.ru/izv2276}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=348044}
\zmath{https://zbmath.org/?q=an:0272.22012}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 3
\pages 497--510
\crossref{https://doi.org/10.1070/IM1973v007n03ABEH001954}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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