Patrick Delorme

Noncommutative Harmonic Analysis: in Honor of Jacques Carmona - Progress in Mathematics Patrick Delorme Softcover Reprint of the Original 1st Ed. 2004 edition

Jacket Description/Back: 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. WallachTable of Contents: Preface * Jacques Carmona * Baldoni-Silva/Vergne: Morris identities and the total residue for a system of type Ar * Barbasch: A reduction theorem for the unitary dual of U(p, q) * Bieliavsky/Pevzner: Symmetric spaces and star representations III. The Poincare disc * Bopp/Rubenthaler: Local zeta functions for a class of symmetric spaces * Bouaziz: Quelques remarques sur les distributions invariantes dans les algebres de Lie reductives * Delorme: Espace des coefficients de representations admissibles d'un groupe reductif p-adique * Harinck/Panichi: Dualite entre G/Gr et le groupe renverse -Gr * Hersant: Sur certains espaces d'homologie relative d'algebres de Lie: cas des polarisations positives * Khalgui/Torasso: La formule de Plancherel pour les groupes de Lie presque algebrique reels * Knapp: Analytic continuation of nonholomorphic discrete series for classical groups * Kostant: A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel Weil theorem * Kuttler/Wallach: Representations of SL2 and the distribution of points in Pn * Libine: A localization argument for characters of reductive Lie groups: an introduction and examples * Lorch/Mantini/Novak: Intertwining ladder representations for SU(p, q) into Dolbeault cohomology * Miller/Schmid: Summation formulas, from Poisson and Voroni to the present * Rossmann: McKay's correspondence and characters of finite subgroups of SU(2) * Torossian: Methodes de Kashiwara Vergne Rouviere pour les espaces symetriques * van den Ban: Einstein integrals and induction of relations"Publisher Marketing: Dedicated to Jacques Carmona, an expert in noncommutative harmonic analysis, the volume presents excellent invited/refereed articles by top notch mathematicians. Topics cover general Lie theory, reductive Lie groups, harmonic analysis and the Langlands program, automorphic forms, and Kontsevich quantization. Good text for researchers and grad students in representation theory.