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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.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
++++ The below data was compiled from various identification fields
in the bibliographic record of this title. This data is provided as
an additional tool in helping to ensure edition identification:
++++ Histoire De La Revolution Francaise Dans Le Departement Du
Gard, Volume 4; Histoire De La Revolution Francaise Dans Le
Departement Du Gard; Francois Rouviere Francois Rouviere A.
Catelan, 1889 History; Europe; France; History / Europe / France
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