Calogero Moser Sutherland Models

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).

Contenu
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.