×

zbMATH — the first resource for mathematics

Unitary representations of Lie groups with cocompact radical and applications. (English) Zbl 0389.22009

MSC:
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
46L05 General theory of \(C^*\)-algebras
22D10 Unitary representations of locally compact groups
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255 – 354. · Zbl 0233.22005 · doi:10.1007/BF01389744 · doi.org
[2] Louis Auslander and Calvin C. Moore, Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc. No. 62 (1966), 199. · Zbl 0204.14202
[3] N. Bourbaki, Eléménts de mathématique. XXVI. Chap. 1: Algébres de Lie, Actualités Sci. Indust., no. 1285, Hermann, Paris, 1960. MR 24 # A2641. · Zbl 0199.35203
[4] Ian D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Norm. Sup. (4) 6 (1973), 407 – 411. · Zbl 0284.57026
[5] Jacques Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. V, Bull. Soc. Math. France 87 (1959), 65 – 79 (French). Jacques Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. VI, Canad. J. Math. 12 (1960), 324 – 352 (French). · Zbl 0171.11702 · doi:10.4153/CJM-1960-028-6 · doi.org
[6] Jacques Dixmier, Les \?*-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). · Zbl 0288.46055
[7] Jacques Dixmier, Sur la représentation régulière d’un groupe localement compact connexe, Ann. Sci. École Norm. Sup. (4) 2 (1969), 423 – 436 (French). · Zbl 0186.46304
[8] Michel Duflo, Sur les extensions des représentations irréductibles des groupes de Lie nilpotents, Ann. Sci. École Norm. Sup. (4) 5 (1972), 71 – 120 (French). · Zbl 0241.22030
[9] James Glimm, Locally compact transformation groups, Trans. Amer. Math. Soc. 101 (1961), 124 – 138. · Zbl 0119.10802
[10] Harish-Chandra, Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc. 76 (1954), 234 – 253. · Zbl 0055.34002
[11] Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 87 – 208. Lecture Notes in Math., Vol. 170. · Zbl 0223.53028
[12] Ronald L. Lipsman, The \?\?\? property for algebraic groups, Amer. J. Math. 97 (1975), no. 3, 741 – 752. · Zbl 0319.22009 · doi:10.2307/2373774 · doi.org
[13] George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265 – 311. · Zbl 0082.11301 · doi:10.1007/BF02392428 · doi.org
[14] Calvin C. Moore and Jonathan Rosenberg, Groups with \?\(_{1}\) primitive ideal spaces, J. Functional Analysis 22 (1976), no. 3, 204 – 224. · Zbl 0328.22014
[15] L. Pukánszky, On the characters and the Plancherel formula of nilpotent groups, J. Functional Analysis 1 (1967), 255 – 280. · Zbl 0165.48603
[16] L. Pukánszky, On the unitary representations of exponential groups, J. Functional Analysis 2 (1968), 73 – 113.
[17] L. Pukánszky, Characters of algebraic solvable groups, J. Functional Analysis 3 (1969), 435 – 494. · Zbl 0186.20004
[18] L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup. (4) 4 (1971), 457 – 608. · Zbl 0238.22010
[19] L. Pukanszky, Action of algebraic groups of automorphisms on the dual of a class of type \? groups, Ann. Sci. École Norm. Sup. (4) 5 (1972), 379 – 395. · Zbl 0263.22011
[20] L. Pukanszky, Characters of connected Lie groups, Acta Math. 133 (1974), 81 – 137. · Zbl 0323.22011 · doi:10.1007/BF02392143 · doi.org
[21] L. Pukanszky, Lie groups with completely continuous representations, Bull. Amer. Math. Soc. 81 (1975), no. 6, 1061 – 1063. · Zbl 0312.22006
[22] Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 19. · Zbl 0265.22022
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.