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The Orbit Method In Geometry And Physics


The Orbit Method In Geometry And Physics
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The Orbit Method In Geometry And Physics


The Orbit Method In Geometry And Physics
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Author : Aleksandr Aleksandrovich Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-05-15

The Orbit Method In Geometry And Physics written by Aleksandr Aleksandrovich Kirillov 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 2003-05-15 with Mathematics categories.


The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.



The Orbit Method In Geometry And Physics


The Orbit Method In Geometry And Physics
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Author : Christian Duval
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Orbit Method In Geometry And Physics written by Christian Duval 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 2012-12-06 with Mathematics categories.


The volume is dedicated to AA. Kirillov and emerged from an international con ference which was held in Luminy, Marseille, in December 2000, on the occasion 6 of Alexandre Alexandrovitch's 2 th birthday. The conference was devoted to the orbit method in representation theory, an important subject that influenced the de velopment of mathematics in the second half of the XXth century. Among the famous names related to this branch of mathematics, the name of AA Kirillov certainly holds a distinguished place, as the inventor and founder of the orbit method. The research articles in this volume are an outgrowth of the Kirillov Fest and they illustrate the most recent achievements in the orbit method and other areas closely related to the scientific interests of AA Kirillov. The orbit method has come to mean a method for obtaining the representations of Lie groups. It was successfully applied by Kirillov to obtain the unitary rep resentation theory of nilpotent Lie groups, and at the end of this famous 1962 paper, it was suggested that the method may be applicable to other Lie groups as well. Over the years, the orbit method has helped to link harmonic analysis (the theory of unitary representations of Lie groups) with differential geometry (the symplectic geometry of homogeneous spaces). This theory reinvigorated many classical domains of mathematics, such as representation theory, integrable sys tems, complex algebraic geometry. It is now a useful and powerful tool in all of these areas.



The Orbit Method In Geometry And Physics


The Orbit Method In Geometry And Physics
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Author : Christian Duval
language : en
Publisher: Birkhäuser
Release Date : 2013-10-03

The Orbit Method In Geometry And Physics written by Christian Duval and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.


The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.



Lectures On The Orbit Method


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.



Lectures On The Orbit Method


Lectures On The Orbit Method
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Author : Aleksandr Aleksandrovich Kirillov
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Lectures On The Orbit Method written by Aleksandr Aleksandrovich Kirillov 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 2004 with Mathematics categories.


Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work 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.



Geometry And Physics


Geometry And Physics
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Author : Fernando Etayo
language : en
Publisher: American Institute of Physics
Release Date : 2009-06

Geometry And Physics written by Fernando Etayo and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06 with Mathematics categories.


These are the 2008 Proceedings of an international workshop that happens every fall since 1992, in Spain or Portugal. It brings together geometers and physicists, to discuss the ideas and developments, in the areas of Lie algebroids, mechanics, Poisson, symplectic, Riemannian and Semi-Riemannian geometries, quantum mechanics, theory of fields, supergravity and supersymmetry.



Representations Of The Infinite Symmetric Group


Representations Of The Infinite Symmetric Group
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Author : Alexei Borodin
language : en
Publisher: Cambridge University Press
Release Date : 2017

Representations Of The Infinite Symmetric Group written by Alexei Borodin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.


An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.



Geometric Methods In Algebra And Number Theory


Geometric Methods In Algebra And Number Theory
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-12

Geometric Methods In Algebra And Number Theory written by Fedor Bogomolov 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 2004-11-12 with Mathematics categories.


* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry



Introduction To Vertex Operator Algebras And Their Representations


Introduction To Vertex Operator Algebras And Their Representations
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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky 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 2012-12-06 with Mathematics categories.


* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.



Perspectives In Analysis Geometry And Topology


Perspectives In Analysis Geometry And Topology
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Author : Ilia Itenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-13

Perspectives In Analysis Geometry And Topology written by Ilia Itenberg 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 2011-12-13 with Mathematics categories.


The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.