By Christian Duval,Laurent Guieu,Valentin Ovsienko
The orbit approach motivated the improvement of a number of parts of arithmetic within the moment 1/2 the 20 th century and continues to be an invaluable and robust device in such parts as Lie idea, illustration thought, integrable platforms, advanced geometry, and mathematical physics. one of the individual names linked to the orbit process is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), areas him because the founding father of orbit thought. the unique study papers during this quantity are written via well-liked mathematicians and mirror fresh achievements in orbit thought and different heavily similar components resembling 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 could be a useful reference for researchers within the above pointed out fields, in addition to an invaluable textual content for graduate seminars and courses.