Geodesic
A~criterion for the decomposability of a~homogeneous representation of a~locally
Izvestiya. Mathematics , Tome 10 (1976) no. 3, pp. 515-533

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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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     author = {M. A. Naimark},
     title = {A~criterion for the decomposability of a~homogeneous representation of a~locally},
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M. A. Naimark. A~criterion for the decomposability of a~homogeneous representation of a~locally. Izvestiya. Mathematics , Tome 10 (1976) no. 3, pp. 515-533. http://geodesic.mathdoc.fr/item/IM2_1976_10_3_a4/