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Description of unitary representations with highest weight for groups $U(p,q)\widetilde{}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 14 (1980) no. 3, pp. 32-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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     author = {G. I. Olshanskii},
     title = {Description of unitary representations with highest weight for groups $U(p,q)\widetilde{}$},
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G. I. Olshanskii. Description of unitary representations with highest weight for groups $U(p,q)\widetilde{}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 14 (1980) no. 3, pp. 32-44. http://geodesic.mathdoc.fr/item/FAA_1980_14_3_a2/

[1] Harish-Chandra, “Representations of semisimple Lie groups. IV”, Amer. J. Math., 77:4 (1955), 743–777 | DOI | MR | Zbl

[2] Harish-Chandra, “Representations of semi-simple Lie groups. VI”, Amer. J. Math., 78:3 (1956), 564–628 | DOI | MR | Zbl

[3] Olshanskii G.I., “Konstruktsiya unitarnykh predstavlenii beskonechnomernykh klassicheskikh grupp”, DAN SSSR, 250:2 (1980), 284–288 | MR

[4] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp i $(r,\infty)$, $SO_0(p,\infty)$, $S_p(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, DAN SSSR, 238:6 (1978), 1295–1298 | MR

[5] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $SO_0(p,\infty)$, $S_p(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, Funkts. analiz, 12:3 (1978), 32–44 | MR

[6] Berezin F.A., “Kvantovanie v kompleksnykh simmetricheskikh prostranstvakh”, Izv. AN SSSR, seriya matem., 39 (1975), 363–402 | MR | Zbl

[7] Gindikin S.G., “Invariantnye obobschennye funktsii v odnorodnykh oblastyakh”, Funkts. analiz, 9:1 (1975), 56–58 | MR | Zbl

[8] Rossi H., Vergne M., “Analytic continuation of the holomorphic discrete series of a semi-simple group”, Acta Math., 136 (1976), 1–59 | DOI | MR | Zbl

[9] Wallach N., “Analytic continuation of the holomorphic discrete series. I, II”, Trans. Amer. Math. Soc., 251, 1979, 1–37 | MR

[10] Parthasarathy R., Criteria for the unitarisability of some highest weight modules, Tata Institute of Fundamental Research, Bombay

[11] Howe R., Remark on classical invariant theory, Yale University, 1976

[12] Sternberg S., “Some recent results on the metaplectic representation”, Lect. Notes in Phys., 79, 1978, 117–144 | DOI | MR

[13] Kashiwara M., Vergne M., “On the Segal–Shale–Weil representations and harmonic polinomials”, Invent. Math., 44:1 (1978), 1–47 | DOI | MR | Zbl

[14] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[15] Jantzen J.C., “Kontravariante Formen auf induzierte Darstellungen halbeinfacher Lie-Algebren”, Math. Ann., 226:1 (1977), 53–65 | DOI | MR | Zbl

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

[17] Gelfand I.M., Graev M.I., “Konechnomernye neprivodimye predstavleniya unitarnoi i polnoi lineinoi gruppy i svyazannye s nimi spetsialnye funktsii”, Izv. AN SSSR, seriya matem., 29 (1965), 1329–1356 | MR