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Softcover ISBN:  9780821820261 
Product Code:  CRMP/22 
List Price:  $108.00 
MAA Member Price:  $97.20 
AMS Member Price:  $86.40 
eBook ISBN:  9781470439361 
Product Code:  CRMP/22.E 
List Price:  $101.00 
MAA Member Price:  $90.90 
AMS Member Price:  $80.80 
Softcover ISBN:  9780821820261 
eBook ISBN:  9781470439361 
Product Code:  CRMP/22.B 
List Price:  $209.00 $158.50 
MAA Member Price:  $188.10 $142.65 
AMS Member Price:  $167.20 $126.80 

Book DetailsCRM Proceedings & Lecture NotesVolume: 22; 1999; 276 ppMSC: Primary 33; Secondary 05; 43; 81
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 representationtheoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate 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

Chapters

Science fiction and Macdonald’s polynomials

On the expansion of elliptic functions and applications

Generalized hypergeometric functions–Classification of identities and explicit rational approximations

Tensor products of $q$superalgebras and $q$series identities. I

$q$Racah polynomials for $BC$ type root systems

Intertwining operators of type $B_N$

Symmetries and continuous $q$orthogonal polynomials

Addition theorems for spherical polynomials on a family of quantum spheres

On a $q$analogue of the string equation and a generalization of the classical orthogonal polynomials

The $q$Bessel function on a $q$quadratic grid

Three statistics on lattice paths

Quantum Grothendieck polynomials

$q$difference raising operators for Macdonald polynomials and the integrality of transition coefficients

Great powers of $q$calculus

$q$special functions: Differentialdifference equations, roots of unity, and all that

On algebras of creation and annihilation operators


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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 representationtheoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.
Titles in this series are copublished 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.

Chapters

Science fiction and Macdonald’s polynomials

On the expansion of elliptic functions and applications

Generalized hypergeometric functions–Classification of identities and explicit rational approximations

Tensor products of $q$superalgebras and $q$series identities. I

$q$Racah polynomials for $BC$ type root systems

Intertwining operators of type $B_N$

Symmetries and continuous $q$orthogonal polynomials

Addition theorems for spherical polynomials on a family of quantum spheres

On a $q$analogue of the string equation and a generalization of the classical orthogonal polynomials

The $q$Bessel function on a $q$quadratic grid

Three statistics on lattice paths

Quantum Grothendieck polynomials

$q$difference raising operators for Macdonald polynomials and the integrality of transition coefficients

Great powers of $q$calculus

$q$special functions: Differentialdifference equations, roots of unity, and all that

On algebras of creation and annihilation operators