Calogero—Moser— Sutherland Models

Front Matter....Pages i-xxv
Classical Dynamical r -Matrices for Calogero—Moser Systems and Their Generalizations....Pages 1-21
Hidden Algebraic Structure of the Calogero—Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog....Pages 23-35
Polynomial Eigenfunctions of the Calogero—Sutherland—Moser Models with Exchange Terms....Pages 37-51
The Theory of Lacunas and Quantum Integrable Systems....Pages 53-64
Canonical Forms for the C -Invariant Tensors....Pages 65-76
 R -Matrices, Generalized Inverses, and Calogero—Moser—Sutherland Models....Pages 77-92
Tricks of the Trade: Relating and Deriving Solvable and Integrable Dynamical Systems....Pages 93-116
Classical and Quantum Partition Functions of the Calogero—Moser—Sutherland Model....Pages 117-125
The Meander Determinant and Its Generalizations....Pages 127-144
Differential Equations for Multivariable Hermite and Laguerre Polynomials....Pages 145-159
Quantum Currents Realization of the Elliptic Quantum Groups E τ,η (sl 2 )....Pages 161-176
Heisenberg—Ising Spin Chain: Plancherel Decomposition and Chebyshev Polynomials....Pages 177-192
Ruijsenaars’s Commuting Difference System from Belavin’s Elliptic R -Matrix....Pages 193-202
Invariants and Eigenvectors for Quantum Heisenberg Chains with Elliptic Exchange....Pages 203-220
The Bispectral Involution as a Linearizing Map....Pages 221-229
On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements....Pages 231-248
Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations....Pages 249-271
Creation Operators for the Calogero—Sutherland Model and Its Relativistic Version....Pages 273-297
New Exact Results for Quantum Impurity Problems....Pages 299-312
Painlevé—Calogero Correspondence....Pages 313-332
Yangian Symmetry in WZW Models....Pages 333-346
The Quantized Knizhnik—Zamolodchikov Equation in Tensor Products of Irreducible sl 2 -Modules....Pages 347-384
Gauge Fields and Interacting Particles....Pages 385-398
Generalizations of Calogero Systems....Pages 399-410
Three-Body Generalizations of the Sutherland Problem....Pages 411-420
On Relativistic Lamé Functions....Pages 421-440
Exact Solution for the Ground State of a One-Dimensional Quantum Lattice Gas with Coulomb—Like Interaction....Pages 441-449
Differential Operators that Commute with the r −2 -type Hamiltonian....Pages 451-459
The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: β = 1, 2, 4....Pages 461-472
Two-Body Elliptic Model in Proper Variables: Lie Algebraic Forms and Their Discretizations....Pages 473-484
Yangian Gelfand—Zetlin Bases, gl N -Jack Polynomials, and Computation of Dynamical Correlation Functions in the Spin Calogero—Sutherland Model....Pages 485-495
Thermodynamics of Moser—Calogero Potentials and Seiberg—Witten Exact Solution....Pages 497-506
New Integrable Generalizations of the CMS Quantum Problem and Deformations of Root Systems....Pages 507-519
The Calogero Model: Integrable Structure and Orthogonal Basis....Pages 521-537
The Complex Calogero—Moser and KP Systems....Pages 539-548
Oscillator 9 j -Symbols, Multdimensional Factorization Method, and Multivariable Krawtchouk Polynomials....Pages 549-561