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...

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...