02986nam a2200385 i 4500991002954629707536m o d cr cnu |||||160726s2014 sz ob 001 0 eng d9783319097732b14259874-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng512.48223AMS 22E30AMS 17B01AMS 22E60AMS 53C35LC QA387.R685Rouvière, François716392Symmetric spaces and the Kashiwara-Vergne method[e-book] /François RouvièreCham [Switzerland] :Springer,20141 online resource (xxi, 196 pages)Lecture Notes in Mathematics,1617-9692 ;2115Includes bibliographical references and indexIntroduction ; Notation ; The Kashiwara-Vergne method for Lie groups ; Convolution on homogeneous spaces ; The role of e-functions ; e-functions and the Campbell Hausdorff formula ; BibliographyGathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's original work for Lie groups. The book includes a complete rewriting of several articles by the author, updated and improved following Alekseev, Meinrenken and Torossian's recent proofs of the conjecture. The chapters are largely independent of each other. Some open problems are suggested to encourage future research. It is aimed at graduate students and researchers with a basic knowledge of Lie theoryLie groupsSymmetric spacesPrinted edition:9783319097725http://link.springer.com/book/10.1007/978-3-319-09773-2An electronic book accessible through the World Wide Web.b1425987403-03-2226-07-16991002954629707536Symmetric spaces and the Kashiwara-Vergne method1388118UNISALENTOle01326-07-16m@ -engsz 00