The chapters in this book treat one of the few classes of problems involving more than one particle for which the equations of quantum mechanics are exactly solvable. These so-called Calogero-Moser- Sutherland models now play a role in research areas in theoretical physics (from soliton theory to statistical mechanics) and mathematics (from representation theory to complex geometry).

Inhalt
1 Classical Dynamical r-Matrices for CalogeroMoser Systems and Their Generalizations.- 2 Hidden Algebraic Structure of the CalogeroSutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog.- 3 Polynomial Eigenfunctions of the CalogeroSutherland Moser Models with Exchange Terms.- 4 The Theory of Lacunas and Quantum Integrable Systems.- 5 Canonical Forms for the C-Invariant Tensors.- 6 R-Matrices, Generalized Inverses, and CalogeroMoser Sutherland Models.- 7 Tricks of the Trade: Relating and Deriving Solvable and Integratile Dynamical Systems.- 8 Classical and Quantum Partition Functions of the CalogeroMoserSutherland Model.- 9 The Meander Determinant and Its Generalizations.- 10 Differential Equations for Multivariable Hermite and Laguerre Polynomials.- 11 Quantum Currents Realization of the Elliptic Quantum Groups E?,?(sl2).- 12 HeisenbergIsing Spin Chain: Plancherel Decomposition and Chebyshev Polynomials.- 13 Ruijsenaars's Commuting Difference System from Belavin's Elliptic R-Matrix.- 14 Invariants and Eigenvectors for Quantum Heisenberg Chains with Elliptic Exchange.- 15 The Bispectral Involution as a Linearizing Map.- 16 On Some Quadratic Algebras: JucysMurphy and Dunkl Elements.- 17 Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations.- 18 Creation Operators for the CalogeroSutherland Model and Its Relativistic Version.- 19 New Exact Results for Quantum Impurity Problems.- 20 PainlevéCalogero Correspondence.- 21 Yangian Symmetry in WZW Models.- 22 The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl2-Modules.- 23 Gauge Fields and Interacting Particles.- 24 Generalizations of Calogero Systems.- 25 Three-Body Generalizations of theSutherland Problem.- 26 On Relativistic Lamé Functions.- 27 Exact Solution for the Ground State of a One-Dimensional Quantum Lattice Gas with CoulombLike Interaction.- 28 Differential Operators that Commute with the r?2-type Hamiltonian.- 29 The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: ? = 1, 2, 4.- 30 Two-Body Elliptic Model in Proper Variables: Lie Algebraic Forms and Their Discretizations.- 31 Yangian GelfandZetlin Bases, glN-Jack Polynomials, and Computation of Dynamical Correlation Functions in the Spin CalogeroSutherland Model.- 32 Thermodynamics of MoserCalogero Potentials and SeibergWitten Exact Solution.- 33 New Integrable Generalizations of the CMS Quantum Problem and Deformations of Root Systems.- 34 The Calogero Model: Integrable Structure and Orthogonal Basis.- 35 The Complex Calogero-Moser and KP Systems.- 36 Oscillator 9j-Symbols, Multidimensional Factorization Method, and Multi variable Krawtchouk Polynomials.