LEADER 02986nam a2200385 i 4500 001 991002954629707536 006 m o d 007 cr cnu ||||| 008 160726s2014 sz ob 001 0 eng d 020 $a9783319097732 035 $ab14259874-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a512.482$223 084 $aAMS 22E30 084 $aAMS 17B01 084 $aAMS 22E60 084 $aAMS 53C35 084 $aLC QA387.R685 100 1 $aRouvière, François$0716392 245 10$aSymmetric spaces and the Kashiwara-Vergne method$h[e-book] /$cFrançois Rouvière 260 $aCham [Switzerland] :$bSpringer,$c2014 300 $a1 online resource (xxi, 196 pages) 440 0$aLecture Notes in Mathematics,$x1617-9692 ;$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$aSymmetric spaces 776 08$aPrinted edition:$z9783319097725 856 40$uhttp://link.springer.com/book/10.1007/978-3-319-09773-2$zAn electronic book accessible through the World Wide Web 907 $a.b14259874$b03-03-22$c26-07-16 912 $a991002954629707536 996 $aSymmetric spaces and the Kashiwara-Vergne method$91388118 997 $aUNISALENTO 998 $ale013$b26-07-16$cm$d@ $e-$feng$gsz $h0$i0 LEADER 00894cam0-2200289 --450 001 9910747298303321 005 20231030115910.0 010 $a978-88-6318-198-2 020 $aIT$b2018-11023 100 $a20231030d2018----kmuy0itay5050 ba 101 0 $aita 102 $aIT 105 $ay 001yy 200 1 $aDonnos terramagnesos$edinamiche di insediamento signorile in Sardegna$eil caso dei Doria (secoli 12.-15.)$fEnrico Basso 210 $aAcireale ; Roma$cBonanno$d2018 215 $a193 p.$d21 cm 225 1 $aSocietà, culture, economia$v1 610 0 $aDoria $aSardegna$aSec. 12.-15. 676 $a945.905$v23$zita 700 1$aBasso,$bEnrico$0274843 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910747298303321 952 $aCOLLEZ 3236 (1)$b966/2023$fFSPBC 959 $aFSPBC 996 $aDonnos terramagnesos$93574484 997 $aUNINA