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008 160726s2014    sz       b    001 0 eng d
020   $a9783319097725
035   $ab14259886-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 0 $a512.482$223
084   $aAMS 22E30
084   $aAMS 17B01
084   $aAMS  22E60
084   $aAMS 53C35
084   $aLC QA387$b.R685
100 1 $aRouvière, François$0716392
245 10$aSymmetric spaces and the Kashiwara-Vergne method /$cFrançois Rouvière
260   $aCham [Switzerland] :$bSpringer,$cc2014
300   $axxi, 196 p. ;$c24 cm
440  0$aLecture notes in mathematics,$x0075-8434 ;$v2115
504   $aIncludes bibliographical references and index
505 0 $aIntroduction ; Notation ; The Kashiwara-Vergne method for Lie groups ; Convolution on homogeneous spaces ; The role of e-functions ; e-functions and the Campbell Hausdorff formula ; Bibliography
520   $aGathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's original work for Lie groups. The book includes a complete rewriting of several articles by the author, updated and improved following Alekseev, Meinrenken and Torossian's recent proofs of the conjecture. The chapters are largely independent of each other. Some open problems are suggested to encourage future research. It is aimed at graduate students and researchers with a basic knowledge of Lie theory
650  0$aLie groups
650  0$aSymmetric spaces
907   $a.b14259886$b17-11-16$c26-07-16
912   $a991002954679707536
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996   $aSymmetric spaces and the Kashiwara-Vergne method$91388118
997   $aUNISALENTO
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