Calogero-Moser Systems and Representation Theory
This small booklet contains lecture notes on the Calogero-Moser integrable system and its relation to other fields of mathematics. In one small place, the reader will find a fascinating kaleidoscope of interesting and modern topics, all interacting with the main theme of the book. The author offers a short description of each subject involved, subjects that include Poisson geometry and Hamiltonian reduction; integrable systems, action-angle variables and the classical and trigonometric Calogero-Moser system; deformation theory of associative algebras and Hochschild cohomology, together with Kontsevich quantization of Poisson structures; quantum momentum maps, quantum Hamiltonian reduction and the Levasseur-Stafford theorem; quantization of the Calogero-Moser system and the Calogero-Moser systems for finite Coxeter groups; Dunkl operators and Olshanetsky-Perelomov Hamiltonians; the rational Cherednik algebra and its relation to double affine Hecke algebras; symplectic reflection algebras and the Koszul deformation principle; the deformation approach to symplectic reflection algebras and, finally, representation theory for rational Cherednik algebras. The exposition still keeps the flavour of the corresponding lectures and it presents in a nice, condensed but understandable form the core of the theory. It really is a remarkable book.