Symmetric Spaces and the Kashiwara-Vergne Method

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Geometry
Cover of the book Symmetric Spaces and the Kashiwara-Vergne Method by François Rouvière, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: François Rouvière ISBN: 9783319097732
Publisher: Springer International Publishing Publication: October 14, 2014
Imprint: Springer Language: English
Author: François Rouvière
ISBN: 9783319097732
Publisher: Springer International Publishing
Publication: October 14, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by François Rouvière
Cover of the book Psychological Mechanisms in Animal Communication by François Rouvière
Cover of the book Obesity by François Rouvière
Cover of the book Popigai Impact Structure and its Diamond-Bearing Rocks by François Rouvière
Cover of the book Competencies in Teaching, Learning and Educational Leadership in the Digital Age by François Rouvière
Cover of the book The Non-Reificatory Approach to Belief by François Rouvière
Cover of the book Image Analysis and Recognition by François Rouvière
Cover of the book Outlooks and Insights on Group Decision and Negotiation by François Rouvière
Cover of the book Netflix and the Re-invention of Television by François Rouvière
Cover of the book Ubiquitous Computing in the Workplace by François Rouvière
Cover of the book Intelligent Comparisons: Analytic Inequalities by François Rouvière
Cover of the book War Crimes Trials and Investigations by François Rouvière
Cover of the book After Marriage in the Long Eighteenth Century by François Rouvière
Cover of the book Hayek: A Collaborative Biography by François Rouvière
Cover of the book The EU's Common Security and Defence Policy by François Rouvière
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy