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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

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}