Symmetric Spaces and the Kashiwara Vergne Method is popular PDF and ePub book, written by François Rouvière in 2014-10-14, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Symmetric Spaces and the Kashiwara Vergne Method can be Read Online from any device for your convenience.
Symmetric Spaces and the Kashiwara Vergne Method Book PDF Summary
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.
Detail Book of Symmetric Spaces and the Kashiwara Vergne Method PDF
- Author : François Rouvière
- Release : 14 October 2014
- Publisher : Springer
- ISBN : 9783319097732
- Genre : Mathematics
- Total Page : 215 pages
- Language : English
- PDF File Size : 14,5 Mb
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