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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.

UDC: 513.88

MSC: Primary 22D12; Secondary 22E45

Received: 24.01.1975

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

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