Lecture Notes in Mathematics

Symmetric Spaces and the Kashiwara-Vergne Method

Authors: Rouviere, Francois

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  • The first introduction to the subject in a self-contained monograph
  • Emphasizes motivations, and links with classical analysis on symmetric spaces
  • Includes a list of open problems
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About this book

Gathering 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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-09773-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $49.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Symmetric Spaces and the Kashiwara-Vergne Method
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2115
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-09773-2
DOI
10.1007/978-3-319-09773-2
Softcover ISBN
978-3-319-09772-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXI, 196
Topics