By Christian Duval,Laurent Guieu,Valentin Ovsienko

The orbit process motivated the improvement of numerous parts of arithmetic within the moment half the 20 th century and continues to be an invaluable and strong software in such parts as Lie conception, illustration thought, integrable platforms, advanced geometry, and mathematical physics. one of the exotic names linked to the orbit strategy is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), locations him because the founding father of orbit thought. the unique learn papers during this quantity are written via favorite mathematicians and mirror contemporary achievements in orbit idea and different heavily similar parts comparable to harmonic research, classical illustration concept, Lie superalgebras, Poisson geometry, and quantization. individuals: 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 paintings can be a useful reference for researchers within the above pointed out fields, in addition to an invaluable textual content for graduate seminars and courses.

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