CRM Proceedings & Lecture Notes 1996; 388 pp; softcover Volume: 9 ISBN10: 0821806017 ISBN13: 9780821806012 List Price: US$119 Member Price: US$95.20 Order Code: CRMP/9
 This book is devoted to a topic that has undergone rapid and fruitful development over the last few years: symmetries and integrability of difference equations and \(q\)difference equations and the theory of special functions that occur as solutions of such equations. Techniques that have been traditionally applied to solve linear and nonlinear differential equations are now being successfully adapted and applied to discrete equations. This volume is based on contributions made by leading experts in the field during the workshop on Symmetries and Integrability of Difference Equations held in Estérel, Québec, in May 1994. Giving an uptodate review of the current status of the field, the book treats these specific topics: Lie group and quantum group symmetries of difference and \(q\)difference equations, integrable and nonintegrable discretizations of continuous integrable systems, integrability of difference equations, discrete Painlevé property and singularity confinement, integrable mappings, applications in statistical mechanics and field theories, YangBaxter equations, \(q\)special functions and discrete polynomials, and \(q\)difference integrable systems. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students, research mathematicians and physicists working in difference equations, special function theory, applications of Lie groups theory, nonlinear phenomena in general and integrability in particular. Also of interest to pure and applied mathematicians, theoretical and mathematical physicists, and engineers interested in solitons. Table of Contents  M. J. Ablowitz, B. M. Herbst, and C. M. Schober  On the numerics of integrable discretizations
 R. A. Askey  A brief introduction to the world of \(q\)
 N. M. Atakishiyev  A Ramanujantype for the AlSalam and Ismail biorthogonal rational functions
 H. M. Babujian and R. Flume  KnizhnikZamolodchikov equations and the algebraic Bethe Ansatz
 H. W. Capel and F. W. Nijhoff  Integrable quantum mappings
 I. Cherdantsev and R. Yamilov  Local master symmetries of differentialdifference equations
 P. A. Clarkson and A. P. Bassom  Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation and their application to discrete equations
 J. F. van Diejen  On the diagonalization of difference CalogeroSutherland systems
 A. Doliwa and P. M. Santini  The integrable dynamics of a discrete curve
 V. Dorodnitsyn  Continuous symmetries of finitedifference evolution equations and grids
 R. Floreanini and L. Vinet  Basic Bessel functions and \(q\)difference equations
 D. V. Fursaev and V. G. Kadyshevsky  Difference equations and gauge symmetry
 H. Frahm, A. R. Its, and V. E. Korepin  An operatorvalued RiemannHilbert problem associated with the XXX model
 F. A. Grunbaum and L. Haine  Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation
 J. P. Harnad  Quantum isomonodromic deformations and the KnizhnikZamolodchikov equations
 N. Joshi and P. J. Vassiliou  Lie symmetries and linearizations of analytic discrete dynamical systems
 E. G. Kalnins and W. Miller  \(q\)algebra representations of the Euclidean, pseudoEuclidean, and oscillator algebras, and their tensor products
 V. B. Kuznetsov  \(_3F_2\)(1) hypergeometric function and quadratic \(R\)matrix algebra
 D. Levi and P. Winternitz  Lie point symmetries of differential difference equations
 R. M. MirKasimov  The factorization method for the differentialdifference relativistic Schrödinger equation and \(q\)deformations
 A. D. Mironov  Quantum deformations of \(\tau\)functions, bilinear identities, and representation theory
 J. Negro  The factorization method and hierarchies of \(q\)oscillator Hamiltonians
 F. W. Nijhoff and G. D. Pang  Discretetime CalogeroMoser model and lattice KP equations
 Y. Ohta, K. Kajiwara, and J. Satsuma  Bilinear structure and exact solutions of the discrete Painlevé I equation
 V. Papageorgiou, B. Grammaticos, and A. Ramani  Integrable difference equations and numerical analysis algorithms
 M. Rahman  An integral representation of the verywellpoised \(_{8{\psi}8}\)
 M. Rahman and S. K. Suslov  Singular analogue of the Fourier transformation for the AskeyWilson polynomials
 A. Ramani, B. Grammaticos, and V. Papageorgiou  Singularity confinement
 A. Ronveaux, S. Belmehdi, E. Godoy, and A. Zarzo  Recurrence relation approach for connection coefficients. Applications to classical discrete orthogonal polynomials
 R. Sahadevan, G. B. Byrnes, and G. R. W. Quispel  Linearisation of difference equations using factorisable Lie symmetries
 A. B. Shabat  First integrals of the infinite Toda lattice
 E. Sorace  Non semisimple quantum groups and ëxponential mappings\"
 V. P. Spiridonov, L. Vinet, and A. S. Zhedanov  Discrete Schrödinger equation, Darboux transformations, and orthogonal polynomials
 L. A. Takhtajan  Integrable cellular automata and AKNS hierarchy
 C. M. Viallet  On some rational Coxeter groups
