Geodesic
A criterion for the decomposability of a homogeneous representation of a locally
Izvestiya. Mathematics, Tome 10 (1976) no. 3, pp. 515-533 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Burbaki N., Topologicheskie vektornye prostranstva, IIL, M., 1959

[2] Shefer X., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[3] Naimark M. A., “Ob odnorodnykh i kvaziodnorodnykh predstavleniyakh lokalno kompaktnoi gruppy”, Dokl. AN SSSR, 205:4 (1972), 783–786 | MR | Zbl

[4] Naimark M. A., “Kriterii neprivodimosti i diskretnoi razlozhimosti odnorodnogo predstavleniya lokalno kompaktnoi gruppy”, Dokl. AN SSSR, 205:5 (1972), 1040–1042 | MR | Zbl

[5] Naimark M. A., “Odnorodnye i kvaziodnorodnye predstavleniya lokalno kompaktnoi gruppy”, Izv. AN SSSR. Ser. matem., 36 (1972), 1020–1048 | MR | Zbl

[6] Naimark M. A., “O pryamom integrale par dvoistvennykh prostranstv”, Dokl. AN SSSR, 217:8 (1974), 762–765 | MR | Zbl

[7] Naimark M. A., “Ob odnorodnykh predstavleniyakh lokalno kompaktnoi gruppy, deistvuyuschikh v pare dvoistvennykh prostranstv”, Dokl. AN SSSR, 220:1 (1975), 38–40 | MR | Zbl

[8] Naimark M. A., “Odnorodnye predstavleniya lokalno kompaktnoi gruppy, deistvuyuschie v pare dvoistvennykh prostranstv”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 134, 1975, 219–234 | MR | Zbl

[9] Naimark M. A., “Pryamoi integral par dvoistvennykh prostranstv”, Izv. AN SSSR Ser. matem., 40 (1976), 355–365 | MR | Zbl

[10] Naimark M. A., “O kriterii razlozhimosti odnorodnogo predstavleniya lokalno kompaktnoi gruppy v pryamoi integral i neprivodimykh predstavlenii”, Dokl. AN SSSR, 233:3 (1975), 566–568 | MR

[11] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl