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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
List of contents
Morris identities and the total residue for a system of type Ar.- A reduction theorem for the unitary dual of U(p, q).- Symmetric spaces and star representations III. The Poincaré disc.- Local zeta functions for a class of symmetric spaces.- Quelques remarques sur les distributions invariantes dans les algèbres de Lie réductives.- Espace des coefficients de représentations admissibles d'un groupe réductif p-adique.- Dualité entre G/G? et Ie groupe renversé ?G?.- Sur certains espaces d'homologie relative d'algèbres de Lie: cas des polarisations positives.- La formule de Plancherel pour les groupes de Lie presque algébrique réels.- Analytic continuation of nonholomorphic discrete series for classical groups.- A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel-Weil theorem.- Representations of SL2and the distribution of points in ?n.- A localization argument for characters of reductive Lie groups: an introduction and examples.- Intertwining ladder representations for SU(p, q)into Dolbeault cohomology.- Summation formulas, from Poisson and Voronoi to the present.- McKay's correspondence and characters of finite subgroups of SU(2).- Méthodes de Kashiwara-Vergne- Rouvière pour les espaces symétriques.- Einstein integrals and induction of relations.
Summary
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.
