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The Orbit Method in Geometry and Physics - In Honor of A.A. Kirillov (Hardcover, 2003 ed.)
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The Orbit Method in Geometry and Physics - In Honor of A.A. Kirillov (Hardcover, 2003 ed.)
Series: Progress in Mathematics, 213
Expected to ship within 10 - 15 working days
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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.
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