Symmetric spaces and the Kashiwara-Vergne method / François Rouvière.

By:

Rouvière, François, 1946- [author.]

Material type: Text

TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2115.Publisher: Cham [Switzerland] : Springer, [2014]Description: 1 online resource (xxi, 196 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783319097732
3319097733

Subject(s):

Additional physical formats: Printed edition:: No titleDDC classification:

512/.482 23

LOC classification:

QA387 .R685 2014eb

Online resources:

Click here to access online

Contents:

Introduction -- 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.

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.

Holdings ( 1 )
Title notes ( 5 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	eBook LN Mathematic		Available

Total holds: 0

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed October 23, 2014).

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.

English.

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