Papers from the Workshop on Symmetries and Integrability of Difference Equations, held May 22-29, 1994, in Esterel, Quebec.

Includes bibliographical references.

On the numerics of integrable discretizations ; A brief introduction to the world of ; A Ramanujan-type for the Al-Salam and Ismail biorthogonal rational functions ; Knizhnik-Zamolodchikov equations and the algebraic Bethe Ansatz ; Integrable quantum mappings ; Local master symmetries of differential-difference equations ; Backlund transformations and hierarchies of exact solutions for the fourth Painleve equation and their application to discrete equations ; On the diagonalization of difference Calogero-Sutherland systems ; The integrable dynamics of a discrete curve ; Continuous symmetries of finite-difference evolution equations and grids ; Basic Bessel functions and difference equations ; Difference equations and gauge symmetry ; An operator-valued Riemann-Hilbert problem associated with the XXX model ; Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation ; Quantum isomonodromic deformations and the Knizhnik-Zamolodchikov equations ; Lie symmetries and linearizations of analytic discrete dynamical systems ; algebra representations of the Euclidean, pseudo-Euclidean, and oscillator algebras, and their tensor products ; 3F_2 1) hypergeometric function and quadratic matrix algebra ; Lie point symmetries of differential difference equations ; The factorization method for the differential-difference relativistic Schrodinger equation and deformations ; Quantum deformations of tau functions, bilinear identities, and representation theory ; The factorization method and hierarchies of oscillator Hamiltonians ; Discrete-time Calogero-Moser model and lattice KP equations ; Bilinear structure and exact solutions of the discrete Painleve I equation ; Integrable difference equations and numerical analysis algorithms ; An integral representation of the very-well-poised 8\psi 8 ; Singular analogue of the Fourier transformation for the Askey-Wilson polynomials ; Singularity confinement ; Recurrence relation approach for connection coefficients. Applications to classical discrete orthogonal polynomials ; Linearisation of difference equations using factorisable Lie symmetries ; First integrals of the infinite Toda lattice ; Non semisimple quantum groups and "exponential mappings" ; Discrete Schrodinger equation, Darboux transformations, and orthogonal polynomials ; Integrable cellular automata and AKNS hierarchy ; On some rational Coxeter groups