LEADER 02852nam a2200349 i 4500 001 991002954679707536 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 945 $aLE013 22E ROU11 (2014)$g1$i2013000293578$lle013$op$pE36.39$q-$rl$s- $t0$u0$v0$w0$x0$y.i15787485$z17-11-16 996 $aSymmetric spaces and the Kashiwara-Vergne method$91388118 997 $aUNISALENTO 998 $ale013$b26-07-16$cm$da $e-$feng$gsz $h0$i0 LEADER 01493nas 2200481-- 450 001 996335816303316 005 20240501213015.0 035 $a(CKB)110978977563811 035 $a(CONSER)cn-77031197- 035 $a(EXLCZ)99110978977563811 100 $a20770907b19762023 --- a 101 0 $aeng 181 $ctxt$2rdacontent 200 00$aCanadian yachting 210 $aToronto $cMaclean-Hunter$d-[2023] 215 $a1 online resource 300 $aPublished: Kerrwil Publications, 1986?-2023. 311 08$aPrint version: Canadian yachting. 0384-0999 (DLC)cn 77031197 (OCoLC)1080290807 531 0 $aCan. yacht. 606 $aYachts and yachting$zCanada$vPeriodicals 606 $aSailing$vPeriodicals 606 $aYachts$zCanada$vPeriodicals 606 $aYachts$zCanada$xPériodiques 606 $aNavigation à voile$xPériodiques 606 $aYachts$2fast 606 $aSailing$2fast 607 $aCanada$2fast$1https://id.oclc.org/worldcat/entity/E39PBJkMHVW4rfVXPrhVP4VwG3 608 $aPeriodicals$2fast 608 $aPeriodicals.$2lcgft 615 0$aYachts and yachting 615 0$aSailing 615 0$aYachts 615 6$aYachts$xPériodiques. 615 6$aNavigation à voile$xPériodiques. 615 7$aYachts 615 7$aSailing 676 $a797.1/24/0971 686 $acci1icc$2lacc 906 $aJOURNAL 912 $a996335816303316 920 $aexl_impl conversion 996 $aCanadian yachting$92409331 997 $aUNISA