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 (booknews.com)

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.Contributors include: 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.

Gives an exposition on the relations among monoidal tensor categories, 3-dimensional topological quantum field theory, and 2-dimensional modular functors. Examples of the category of representations of a quantum group at a root of unit, and the Wess-Zumino-Witten modular functor, are discussed in detail. Chapters cover braided tensor, ribbon, and modular tensor categories, 3-dimensional topological quantum field theory, and moduli spaces and complex modular functors. Can be used as a text at the advanced graduate level. Annotation c. Book News, Inc., Portland, OR (booknews.com)

La chiesa ortodossa russa dal 1943 ai nostri giorni: una storia di martirio e di persecuzione, una preziosa ereditą per i cristiani del XXI secolo

In 13 lectures by three authors admittedly afflicted with ' q -disease' (i.e. infatuation with the mathematical structures of conformal field theory and their q -deformations), they wax eruditely on this new area of theoretical physics and its powerful tools at the interface between mathematics and physics. Titles include: free field realization, quantum affine algebras, connection matrices for the quantum K-Z equations and elliptic functions, and current developments and future perspectives. Intended for those familiar with the representation theory of simple Lie algebras. Annotation c. by Book News, Inc., Portland, Or.