×

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
PDF BibTeX XML Cite
Full Text: DOI

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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.