The Orbit Method In Geometry And Physics
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| Author | : Christian Duval |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 478 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200296 |
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.
| Author | : Aleksandr Aleksandrovich Kirillov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 434 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835300 |
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.
| Author | : Aleksandr Aleksandrovich Kirillov |
| Publisher | : |
| Total Pages | : 408 |
| Release | : 1900 |
| Genre | : Lie groups |
| ISBN | : 9781470417994 |
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.
| Author | : Jerrold E. Marsden |
| Publisher | : SIAM |
| Total Pages | : 103 |
| Release | : 1981-01-01 |
| Genre | : Science |
| ISBN | : 0898711703 |
A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.
| Author | : Dino Boccaletti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3662033194 |
Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... J Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).
| Author | : Dino Boccaletti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3662092409 |
Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... ] Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).
| Author | : Alexandre V. Borovik |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 282 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461220661 |
Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
| Author | : Edgar Lee Stout |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 454 |
| Release | : 2007-07-28 |
| Genre | : Mathematics |
| ISBN | : 0817645381 |
This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions of uniform approximation for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. The book also discusses important applications and motivates the reader with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.
| Author | : James Lepowsky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 330 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681868 |
* 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.
| Author | : Juan-Pablo Ortega |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 526 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475738110 |
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
