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Zbl pre05131085
Etingof, Pavel
Calogero-Moser systems and representation theory. (English)
[B] Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society Publishing House. ix, 92~p. EUR~28.00 (2007). ISBN 3-03719-034-0/pbk

Preliminary review / Publisher's description: Calogero -Moser systems, which were originally discovered by specialists in integrable systems are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero -Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, we give short introductions to each of the subjects involved, and provide a number of exercises.\par The book will be suitable for mathematics graduate students and researchers in the areas of representation theory, noncommutative algebra, algebraic geometry, and related areas.
MSC 2000:
*53D17 Poisson manifolds
16G30 Representations of orders, etc. over commutative rings
17B80 Applications of Lie algebras to integrable systems
37J35 Completely integrable systems, etc.
53D20 Momentum maps; symplectic reduction
53D55 Deformation quantization, star products
81R12 Relations with integrable systems

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Highlights
Scientific prize winners of the ICM 2010
Overhang
Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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