A.A. Kirillov's pioneering 1962 paper on nilpotent orbits places him as the founder of orbit theory. 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. In this volume, prominent contributors present original and expository invited papers in the areas of Lie theory, geometry, algebra, and mathematical physics. An invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

A wide collection of recent research articles describing the most recent developments in representation theory and related topics Researchers will find in this volume a representative and "state-of-the-art" literature and references These articles are written by the most distinguished and active mathematicians in the subject

Inhalt
A Principle of Variations in Representation Theory.- Finite Group Actions on Poisson Algebras.- Representations of Quantum Tori and G-bundles on Elliptic Curves.- Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I.- Brèves remarques sur l'oeuvre de A. A. Kirillov.- Gerbes of Chiral Differential Operators. III.- Defining Relations for the Exceptional Lie Superalgebras of Vector Fields.- Schur-Weyl Duality and Representations of Permutation Groups.- Quantization of Hypersurface Orbital Varieties insln.- Generalization of a Theorem of Waldspurger to Nice Representations.- Two More Variations on the Triangular Theme.- The Generalized Cayley Map from an Algebraic Group to its Lie Algebra.- Geometry ofGLn(?)at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary.- Why Would Multiplicities be Log-Concave?.- Point Processes Related to the Infinite Symmetric Group.- Some Toric Manifolds and a Path Integral.- Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces.- Maximal Subalgebras of the Classical Linear Lie Superalgebras.