Topic #14 --------------- OP-SF NET ---------------- November 15, 1996 ~~~~~~~~~ From: Tom Koornwinder Subject: Announcement of edited book on Symmetries and Integrability of Difference Equations Symmetries and Integrability of Difference Equations Edited by: Decio Levi, Luc Vinet and Pavel Winternitz CRM Proceedings & Lecture Notes Vol.9 American Mathematical Society, 1996 ISBN: 0-8218-0601-7 This book is devoted to 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 adapted and applied to discrete equations. This volume is based on contributions during the workshop on Symmetries and Integrability of Difference Equations held in Esterel, Quebec, in May 1994. 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 Painleve property and singularity confinement - integrable mappings - applications in statistical mechanics and field theories - Yang-Baxter equations - q-special functions and discrete polynomials - q-difference integrable systems Contents * M. J. Ablowitz, B. M. Herbst, and C. Schober -- On the numerics of integrable discretizations * R. Askey -- A brief introduction to the world of q * N. M. Atakishiyev -- A Ramanujan-type measure for the Al-Salam and Ismail biorthogonal rational functions * H. M. Babujian and R. Flume -- Knizhnik-Zamolodchikov 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 differential-difference equations * P. A. Clarkson and A. P. Bassom -- Backlund transformations and hierarchies of exact solutions for the fourth Painleve equation and their application to discrete equations * J. F. van Diejen -- On the diagonalization of difference Calogero-Sutherland systems * A. Doliwa and P. M. Santini -- The integrable dynamics of a discrete curve * V. Dorodnitsyn -- Continuous symmetries of finite-difference 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 operator-valued Riemann-Hilbert problem associated with the XXX model * F. A. Grunbaum and L. Haine -- Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation * J. Harnad -- Quantum isomonodromic deformations and the Knizhnik-Zamolodchikov equations * N. Joshi and P. J. Vassiliou -- Lie symmetries and linearizations of analytic discrete dynamical systems * E. G. Kalnins and W. Miller, Jr. -- q-Algebra representations of the Euclidean, pseudo-Euclidean and oscillator algebras, and their tensor products * V. B. Kuznetsov -- 3F2(1) hypergeometric function and quadratic R-matrix algebra * D. Levi and P. Winternitz -- Lie point symmetries of differential difference equations * R. M. Mir-Kasimov -- The factorization method for the differential-difference relativistic Schrodinger equation and q-deformations * A. 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 -- Discrete-time Calogero-Moser model and lattice KP equations * Y. Ohta, K. Kajiwara, and J. Satsuma -- Bilinear structure and exact solutions of the discrete Painleve I equation * V. Papageorgiou, B. Grammaticos, and A. Ramani -- Integrable difference equations and numerical analysis algorithms * M. Rahman -- An integral representation of the very-well-poised 8psi8 series * M. Rahman and S. K. Suslov -- Singular analogue of the Fourier transformation for the Askey-Wilson 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 "Exponential Mappings" * V. Spiridonov, L. Vinet, and A. Zhedanov -- Discrete Schrodinger equation, Darboux transformations, and orthogonal polynomials * L. A. Takhtajan -- Integrable cellular automata and AKNS hierarchy * C. M. Viallet -- On some rational Coxeter groups

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