02593nam 22004575a 450 991015193680332120091109150325.03-03719-534-710.4171/034(CKB)3710000000953807(CH-001817-3)52-091109(PPN)178155187(EXLCZ)99371000000095380720091109j20070303 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierCalogero-Moser systems and representation theory[electronic resource] /Pavel EtingofZuerich, Switzerland European Mathematical Society Publishing House20071 online resource (101 pages)Zurich Lectures in Advanced Mathematics (ZLAM)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. The book will be suitable for mathematics graduate students and researchers in the areas of representation theory, noncommutative algebra, algebraic geometry, and related areas.Groups & group theorybicsscAnalytic geometrybicsscAssociative rings and algebrasmscAlgebraic geometrymscMechanics of particles and systemsmscGroups & group theoryAnalytic geometryAssociative rings and algebrasAlgebraic geometryMechanics of particles and systems16-xx14-xx70-xxmscEtingof Pavel1071533ch0018173BOOK9910151936803321Calogero-Moser systems and representation theory2567448UNINA