Geodesic
A description of the quasi-simple irreducible representations of the groups $U(n,1)$ and $\operatorname{Spin}(n,1)$
Izvestiya. Mathematics, Tome 11 (1977) no. 1, pp. 31-50 
D. P. Zhelobenko. A description of the quasi-simple irreducible representations of the groups $U(n,1)$ and $\operatorname{Spin}(n,1)$. Izvestiya. Mathematics, Tome 11 (1977) no. 1, pp. 31-50. http://geodesic.mathdoc.fr/item/IM2_1977_11_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article deals with a family of elementary $G$-modules $E(\sigma)$, where $G$ is either one of the groups $U(n,1)$, with $n>1$, or one of the groups $\operatorname{Spin}(n,1)$, wit $n>2$. A description is given of all of the submodules of $E(\sigma)$; in addition, these submodules are characterized in terms of the kernels and images of the intertwining operators (symmetry operators). A description is given of all of the factors of $E(\sigma)$ up to isomorphism. It follows from these results that every quasi-simple irreducible Banach $G$-module is infinitesimally equivalent to a submodule of some $E(\sigma)$. Bibliography: 9 titles.

[1] Zhelobenko D. P., Garmonicheskii analiz na poluprostykh kompleksnykh gruppakh Li, Nauka, M., 1974 | MR | Zbl

[2] Zhelobenko D. P., “Operatory diskretnoi simmetrii dlya reduktivnykh grupp Li”, Izvestiya AN SSSR. Ser. matem., 40 (1976), 1055–1083 | Zbl

[3] Zhelobenko D. P., Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[4] Klymyk A. V., Shirokov V. A., Representations of Lie groups $U(n,1)$, $IU(n)$ and their algebras, I, II, preprint, Kiev, 1974

[5] Knapp A. W., Stein E. M., “Interwining operators for semi-simple groups”, Ann. Math., 93 (1971), 489–578 | DOI | MR | Zbl

[6] Kraljevič H., “Representations of the universal covering group of the group $U(n,1)$”, Glasnik Mat., 8 (1973), 23–72 | Zbl

[7] Lepowsky J., “Algebraic results on representations of semi-simple Lie groups”, Trans. Amer. Math. Soc., 176 (1973), 1–44 | DOI | MR | Zbl

[8] Thieleker E., “On the quasi-simple irreducible representations of the Lorentz groups”, Trans. Amer. Math. Soc., 179 (1973), 465–505 | DOI | MR | Zbl

[9] Schiffmann G., “Intégrales d'entrelacement”, C. R. Acad. Sci. Paris Sér. A-B, 266 (1968), A47–A49 | MR