SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

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

The book treats these specific topics:
- Lie group and quantum group symmetries of difference and q-difference
- integrable and nonintegrable discretizations of continuous integrable
- 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


   * 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
   * V. Dorodnitsyn -- Continuous symmetries of finite-difference
     evolution equations and grids
   * R. Floreanini and L. Vinet -- Basic Bessel functions and q-difference
   * D. V. Fursaev and V. G. Kadyshevsky -- Difference equations and gauge
   * 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
   * 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
   * A. Mironov -- Quantum deformations of tau-functions, bilinear
     identities and representation theory
   * J. Negro -- The factorization method and hierarchies of q-oscillator
   * 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
   * 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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