EAN: 9783319097725

SYMMETRIC SPACES AND THE KASHIWARA-VERGNE METHO...

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.

Aktuelle Preise zur EAN 9783319097725

Produktinformationen zur 9783319097725