| The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov 2003 Edition Contributor(s): Duval, Christian (Author), Guieu, Laurent (Author), Ovsienko, Valentin (Author) |
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ISBN: 0817642323 ISBN-13: 9780817642327 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: May 2003 Annotation: The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and continues to be an important tool today. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits in 1962, places him as the founder of orbit theory. The origins of the orbit method lie in the search for a relationship between classical and quantum mechanics. Over the years, the orbit method has been used to link harmonic analysis (theory of unitary representations of Lie groups) with differential geometry (symplectic geometry of homogeneous spaces), and it has stimulated and invigorated many classical domains of mathematics, i.e., representation theory, integrable systems, complex algebraic geometry, to name several. It continues to be a useful and powerful tool in all of these areas of mathematics and mathematical physics. This volume, dedicated to A. A. Kirillov, covers a very broad range of key topics such as: * The orbit method in the theory of unitary representations of Lie groups * Infinite-dimensional Lie groups: their orbits and representations * Quantization and the orbit method; geometric quantization (old and new) * The Virasoro algebra; string and conformal field theories * Lie superalgebras and their representations * Combinatorial aspects of representation theory. The prominent contributors to this volume present original and expository invited papers in the areas of Lie theory, geometry, algebra, and mathematical physics. 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. Contributorsinclude: A. Alekseev, J. Alev, R. Brylinski, J. Dixmier, 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, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Medical - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| LCCN: 2003041933 |
| Series: Progress in Mathematics |
| Physical Information: 1.1" H x 6.26" W x 9.6" (1.88 lbs) 474 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |