000 03714nam a22005175i 4500
001 978-3-319-09773-2
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005 20190213151054.0
007 cr nn 008mamaa
008 141014s2014 gw | s |||| 0|eng d
020 _a9783319097732
_9978-3-319-09773-2
024 7 _a10.1007/978-3-319-09773-2
_2doi
050 4 _aQA403-403.3
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.785
_223
100 1 _aRouvière, François.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSymmetric Spaces and the Kashiwara-Vergne Method
_h[electronic resource] /
_cby François Rouvière.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXXI, 196 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2115
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 _aHarmonic analysis.
650 0 _aGlobal differential geometry.
650 0 _aAlgebra.
650 0 _aGlobal analysis.
650 1 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aNon-associative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11116
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319097749
776 0 8 _iPrinted edition:
_z9783319097725
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2115
856 4 0 _uhttps://doi.org/10.1007/978-3-319-09773-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9417
_d9417