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Algebraic Methods and \(q\)-Special Functions
Edited by: Jan Felipe van Diejen, Universidad de Chile, Santiago, Chile, and Luc Vinet, Université de Montréal, Québec, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Proceedings & Lecture Notes
1999; 276 pp; softcover
Volume: 22
ISBN-10: 0-8218-2026-5
ISBN-13: 978-0-8218-2026-1
List Price: US$96
Member Price: US$76.80
Order Code: CRMP/22
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There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods.

The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Graduate students and research mathematicians interested in special functions, combinatorics, representation theory, harmonic analysis, quantum groups, integrable systems, and mathematical physics; theoretical physicists.

Table of Contents

  • F. Bergeron and A. M. Garsia -- Science fiction and Macdonald's polynomials
  • R. Chouikha -- On the expansion of elliptic functions and applications
  • D. V. Chudnovsky and G. V. Chudnovsky -- Generalized hypergeometric functions-Classification of identities and explicit rational approximations
  • W. S. Chung, E. G. Kalnins, and W. Miller, Jr. -- Tensor products of \(q\)-superalgebras and \(q\)-series identities. I
  • J. F. van Diejen and J. V. Stokman -- \(q\)-Racah polynomials for \(BC\) type root systems
  • C. F. Dunkl -- Intertwining operators of type \(B_N\)
  • R. Floreanini, J. LeTourneux, and L. Vinet -- Symmetries and continuous \(q\)-orthogonal polynomials
  • P. G. A. Floris -- Addition theorems for spherical polynomials on a family of quantum spheres
  • F. A. Grünbaum and L. Haine -- On a \(q\)-analogue of the string equation and a generalization of the classical orthogonal polynomials
  • M. E. H. Ismail, D. R. Masson, and S. K. Suslov -- The \(q\)-Bessel function on a \(q\)-quadratic grid
  • D. Kim and D. Stanton -- Three statistics on lattice paths
  • A. N. Kirillov -- Quantum Grothendieck polynomials
  • A. N. Kirillov and M. Noumi -- \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients
  • B. A. Kupershmidt -- Great powers of \(q\)-calculus
  • V. Spiridonov -- \(q\)-special functions: Differential-difference equations, roots of unity, and all that
  • A. Strasburger -- On algebras of creation and annihilation operators
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