Ebook: Noncommutative Harmonic Analysis: In Honor of Jacques Carmona

This volume is devoted to the theme of Noncommutative Harmonic Analysis and consists of articles in honor of Jacques Carmona, whose scientific interests range through all aspects of Lie group representations. The topics encompass the theory of representations of reductive Lie groups, and especially the determination of the unitary dual, the problem of geometric realizations of representations, harmonic analysis on reductive symmetric spaces, the study of automorphic forms, and results in harmonic analysis that apply to the Langlands program.

General Lie groups are also discussed, particularly from the orbit method perspective, which has been a constant source of inspiration for both the theory of reductive Lie groups and for general Lie groups. Also covered is Kontsevich quantization, which has appeared in recent years as a powerful tool.

Contributors: V. Baldoni-Silva; D. Barbasch; P. Bieliavsky; N. Bopp; A. Bouaziz; P. Delorme; P. Harinck; A. Hersant; M.S. Khalgui; A.W. Knapp; B. Kostant; J. Kuttler; M. Libine; J.D. Lorch; L.A. Mantini; S.D. Miller; J.D. Novak; M.-N. Panichi; M. Pevzner; W. Rossmann; H. Rubenthaler; W. Schmid; P. Torasso; C. Torossian; E.P. van den Ban; M. Vergne; and N.R. Wallach

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Content:
Front Matter....Pages i-xvii
Morris identities and the total residue for a system of type A r ....Pages 1-19
A reduction theorem for the unitary dual of U(p,q)....Pages 21-60
Symmetric spaces and star representations III. The Poincar? disc....Pages 61-77
Local zeta functions for a class of symmetric spaces....Pages 79-118
Quelques remarques sur les distributions invariantes dans les alg?bres de Lie r?ductives....Pages 119-130
Espace des coefficients de repr?sentations admissibles d’un groupe r?ductif p-adique....Pages 131-176
Dualit? entre G/G ? et le groupe renvers? ? G ? ....Pages 177-199
Sur certains espaces d’homologie relative d’alg?bres de Lie: cas des polarisations positives....Pages 201-212
La formule de Plancherel pour les groupes de Lie presque alg?briques r?els....Pages 213-251
Analytic continuation of nonholomorphic discrete series for classical groups....Pages 253-289
A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel-Weil theorem....Pages 291-353
Representations of SL 2 and the distribution of points in ? n ....Pages 355-373
A localization argument for characters of reductive Lie groups: an introduction and examples....Pages 375-393
Intertwining ladder representations for SU(p, q) into Dolbeault cohomology....Pages 395-418
Summation formulas, from Poisson and Voronoi to the present....Pages 419-440
McKay’s correspondence and characters of finite subgroups of SU(2)....Pages 441-458
M?thodes de Kashiwara-Vergne-Rouvi?re pour les espaces sym?triques....Pages 459-486
Eisenstein integrals and induction of relations....Pages 487-509

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Content:
Front Matter....Pages i-xvii
Morris identities and the total residue for a system of type A r ....Pages 1-19
A reduction theorem for the unitary dual of U(p,q)....Pages 21-60
Symmetric spaces and star representations III. The Poincar? disc....Pages 61-77
Local zeta functions for a class of symmetric spaces....Pages 79-118
Quelques remarques sur les distributions invariantes dans les alg?bres de Lie r?ductives....Pages 119-130
Espace des coefficients de repr?sentations admissibles d’un groupe r?ductif p-adique....Pages 131-176
Dualit? entre G/G ? et le groupe renvers? ? G ? ....Pages 177-199
Sur certains espaces d’homologie relative d’alg?bres de Lie: cas des polarisations positives....Pages 201-212
La formule de Plancherel pour les groupes de Lie presque alg?briques r?els....Pages 213-251
Analytic continuation of nonholomorphic discrete series for classical groups....Pages 253-289
A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel-Weil theorem....Pages 291-353
Representations of SL 2 and the distribution of points in ? n ....Pages 355-373
A localization argument for characters of reductive Lie groups: an introduction and examples....Pages 375-393
Intertwining ladder representations for SU(p, q) into Dolbeault cohomology....Pages 395-418
Summation formulas, from Poisson and Voronoi to the present....Pages 419-440
McKay’s correspondence and characters of finite subgroups of SU(2)....Pages 441-458
M?thodes de Kashiwara-Vergne-Rouvi?re pour les espaces sym?triques....Pages 459-486
Eisenstein integrals and induction of relations....Pages 487-509
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