## On the existence and irreducibility of certain series of representations.(English)Zbl 0229.22026

### MSC:

 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods 22E10 General properties and structure of complex Lie groups 43A90 Harmonic analysis and spherical functions
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### References:

 [1] François Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97 – 205 (French). · Zbl 0074.10303 [2] Harish-Chandra, Representations of a semisimple Lie group on a Banach space. I, Trans. Amer. Math. Soc. 75 (1953), 185 – 243. · Zbl 0051.34002 [3] I. M. Gel$$^{\prime}$$fand and M. I. Graev, Unitary representations of the real unimodular group (principal nondegenerate series), Amer. Math. Soc. Transl. (2) 2 (1956), 147 – 205. · Zbl 0070.26102 [4] D. A. Kajdan, Sur les relations entre l’espace dual d’un groupe et la structure de ses sous-groupes fermés, Funkcional. Anal. i Priložen. 1 (1967), 71-74. [5] Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327 – 404. · Zbl 0124.26802 [6] Bertram Kostant and Stephen Rallis, On representations associated with symmetric spaces, Bull. Amer. Math. Soc. 75 (1969), 884 – 888. · Zbl 0223.53050 [7] Bertram Kostant and Stephen Rallis, On orbits associated with symmetric spaces, Bull. Amer. Math. Soc. 75 (1969), 879 – 883. · Zbl 0223.53049 [8] Edward Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572 – 615. · Zbl 0091.10704 [9] K. R. Parthasarathy, R. Ranga Rao, and V. S. Varadarajan, Representations of complex semi-simple Lie groups and Lie algebras, Ann. of Math. (2) 85 (1967), 383 – 429. · Zbl 0177.18004
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