Lectures on the Orbit Method

by A.A. Kirillov

The orbit method is a useful tool in areas such as Lie theory, group representations, integrable systems, and mathematical physics. Kirillov, who introduced the orbit method in the 1960s, provides a self-contained exposition of the orbit method for non-experts. The book can be used as a text for a graduate course, a handbook for non- experts, and a reference for research mathematicians and mathematical physicists. Annotation © 2004 Book News, Inc., Portland, OR

408 pages, Hardcover

First published August 1, 2004

About the author

Alexandre Aleksandrovich Kirillov
(Алекса́ндр Алекса́ндрович Кири́ллов)

Reviews

[Andrew]

The philosophy is fascinating. Symplectic G-manifolds correspond to classical mechanical systems with G symmetries. Unitary representations of G correspond to quantum mechanical systems with G symmetries. Since g* is the final object in the category of Poisson G-manifolds, we should expect its space of leaves in the symplectic foliation by coadjoint orbits to parametrize irreducible unitary representations IF a sufficiently good notion of "quantization" of a classical mechanical system is possible.