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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 544–561 (Mi izv2141)  

A criterion for the decomposability of a homogeneous representation of a locally compact group into a direct integral of its irreducible representations

M. A. Naimark


Abstract: Sufficient conditions are obtained for the decomposability of a homogeneous representation of a locally compact group into a direct integral of its irreducible representations in terms of the associated algebra of the representation. These results are then applied to homogeneous representations of connected complex semisimple Lie groups.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 515–533

Bibliographic databases:

UDC: 513.88
MSC: Primary 22D12; Secondary 22E45
Received: 24.01.1975

Citation: M. A. Naimark, “A criterion for the decomposability of a homogeneous representation of a locally compact group into a direct integral of its irreducible representations”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 544–561; Math. USSR-Izv., 10:3 (1976), 515–533

Citation in format AMSBIB
\Bibitem{Nai76}
\by M.~A.~Naimark
\paper A~criterion for the decomposability of a~homogeneous representation of a~locally
compact group into a~direct integral of its irreducible representations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 3
\pages 544--561
\mathnet{http://mi.mathnet.ru/izv2141}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=419674}
\zmath{https://zbmath.org/?q=an:0343.22007}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 3
\pages 515--533
\crossref{https://doi.org/10.1070/IM1976v010n03ABEH001715}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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