@article{IM2_1971_5_3_a5,
author = {D. P. Zhelobenko},
title = {Classification of extremally irreducible and normally irreducible representations of semisimple complex connected {Lie} groups},
journal = {Izvestiya. Mathematics},
pages = {589--613},
year = {1971},
volume = {5},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/}
}
TY - JOUR AU - D. P. Zhelobenko TI - Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups JO - Izvestiya. Mathematics PY - 1971 SP - 589 EP - 613 VL - 5 IS - 3 UR - http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/ LA - en ID - IM2_1971_5_3_a5 ER -
D. P. Zhelobenko. Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups. Izvestiya. Mathematics, Tome 5 (1971) no. 3, pp. 589-613. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/
[1] Berezin F. A., “Operatory Laplasa na poluprostykh gruppakh Li”, Tr. Mosk. matem. ob-va, 6 (1957), 371–463 | MR | Zbl
[2] Burbaki N., Topologicheskie vektornye prostranstva, IL, M., 1959
[3] Gelfand I. M., Vilenkin N. Ya., Graev M. I., Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Obobschennye funktsii, 5, Fizmatgiz, M., 1962 | MR
[4] Godement R ., “A theory of spherical functions. I”, Trans. Amer. Math. Soc., 73:3 (1952), 496–556 ; Godman R., Matematika, 5:5 (1961), 55–87 | DOI | MR | Zbl
[5] Zhelobenko D. P., “Simmetriya v klasse elementarnykh predstavlenii poluprostoi kompleksnoi gruppy Li”, Funktsionalnyi analiz i ego prilozheniya, 1:2 (1967), 15–38 | MR
[6] Zhelobenko D. P., “Analiz neprivodimosti v klasse elementarnykh predstavlenii poluprostoi kompleksnoi svyaznoi gruppy Li”, Izv. AN SSSR. Ser. matem., 32 (1968), 108–133
[7] Zhelobenko D. P., “Operatsionnoe ischislenie na poluprostoi kompleksnoi gruppe Li”, Izv. AN SSSR. Ser. matem., 33 (1969), 931–973
[8] Zhelobenko D. P., “Garmonicheskii analiz funktsii na poluprostoi kompleksnoi gruppe Li. II”, Izv. AN SSSR. Ser. matem., 33 (1969), 1255–1295 | Zbl
[9] Zhelobenko D. P., Naimark M. A., “Opisanie vpolne neprivodimykh predstavlenii poluprostoi kompleksnoi gruppy Li”, Izv. AN SSSR. Ser. matem., 34 (1970), 57–85
[10] Zhelobenko D. P., “Analog teorii Kartana–Veilya dlya beskonechnomernykh predstavlenii poluprostoi kompleksnoi gruppy Li”, Dokl. AN SSSR, 175:1 (1967), 24–27
[11] Zhelobenko D. P., “K teorii lineinykh predstavlenii kompleksnykh i veschestvennykh grupp Li”, Tr. Mosk. matem. ob-va, 12 (1963), 53–98
[12] Zhelobenko D. P., “O beskonechno differentsiruemykh vektorakh v teorii predstavlenii”, Vestn. Mosk. un-ta, 1965, no. 1, 3–10
[13] Zhelobenko D. P., “O predstavleniyakh klassa 0 poluprostoi kompleksnoi gruppy Li”, Funktsionalnyi analiz i ego prilozheniya, 4:2 (1970), 85–86 | MR | Zbl
[14] Kaplansky I., “Groups with representations of bounded degree”, Canadian J. Math., 1 (1949), 105–112 | MR | Zbl
[15] Kostant B., “The existence and irreducibility of certain series of representations”, Bull. Amer. Math. Soc., 76 (1969), 68–93 | MR
[16] Mackey G. W., “Infinite dimensional group representations”, Colloqium lecture given at Stillwater (Oklachoma, August, 1961); Matematika, 6:5 (1962), 57–103 | MR
[17] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl
[18] Teoriya algebr Li. Topologiya grupp Li, Seminar “Sofus Li”, IL, M., 1962
[19] Harish-Chandra, “Representations of semi-simple Lie groups on a Banach space. I”, Trans. Amer. Math. Soc., 75 (1953), 185–243 ; “II”, 76 (1954), 26–65 | DOI | MR | Zbl | DOI | MR | Zbl
[20] Helgason S., “Application of the Radon transform to representations of semi-simple Lie groups”, Proc. Nat. Acad. Sci. USA, 60 (1969), 3–6