Symmetric Spaces And The Kashiwara Vergne Method
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Symmetric Spaces And The Kashiwara Vergne Method
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Author : François Rouvière
language : en
Publisher: Springer
Release Date : 2014-10-14
Symmetric Spaces And The Kashiwara Vergne Method written by François Rouvière and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Mathematics categories.
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.
Symmetric Spaces And The Kashiwara Vergne Method
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Author : Francois Rouviere
language : en
Publisher: Springer
Release Date : 2014-10-19
Symmetric Spaces And The Kashiwara Vergne Method written by Francois Rouviere and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-19 with Mathematics categories.
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.
Geometric Analysis On Symmetric Spaces
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Author : Phillip Griffiths
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Geometric Analysis On Symmetric Spaces written by Phillip Griffiths and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Education categories.
"This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations - that is, representations on solution spaces of invariant differential equations."--BOOK JACKET.
Geometric Analysis On Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-27
Geometric Analysis On Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-27 with Mathematics categories.
This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations?that is, representations on solution spaces of invariant differential equations. Known for his high-quality expositions, Helgason received the 1988 Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups.
Representation Theory And Harmonic Analysis On Symmetric Spaces
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Author : Jens Gerlach Christensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-27
Representation Theory And Harmonic Analysis On Symmetric Spaces written by Jens Gerlach Christensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-27 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Representation Of Lie Groups And Special Functions
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Author : N.Ja. Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Representation Of Lie Groups And Special Functions written by N.Ja. Vilenkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
The Orbit Method In Representation Theory
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Author : Dulfo
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-01-01
The Orbit Method In Representation Theory written by Dulfo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Ever since its introduction around 1960 by Kirillov, the orbit method has played a major role in representation theory of Lie groups and Lie algebras. This book contains the proceedings of a conference held from August 29 to September 2, 1988, at the University of Copenhagen, about "the orbit method in representation theory." It contains ten articles, most of which are original research papers, by well-known mathematicians in the field, and it reflects the fact that the orbit method plays an important role in the representation theory of semisimple Lie groups, solvable Lie groups, and even more general Lie groups, and also in the theory of enveloping algebras.
Lectures On The Orbit Method
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Author : A. A. Kirillov
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-21
Lectures On The Orbit Method written by A. A. Kirillov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-21 with Mathematics categories.
Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which deciphers to the sentence ?It is worthwhile to solve differential equations?. Accordingly, one can express the main idea behind the Orbit Method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient ?User's Guide? and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.
Group Theoretical Methods In Physics
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Author : M. A. Markov
language : en
Publisher: CRC Press
Release Date : 1985
Group Theoretical Methods In Physics written by M. A. Markov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.