Algebraic Methods and
qSpecial Functions
Edited by: Jan Felipe van Diejen, Universidad de Chile, Santiago,
Chile, and Luc Vinet, Université de Montréal,
Québec, PQ, Canada
Description
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.
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 functionsClassification
of identities and explicit rational approximations

W. S. Chung, E. G. Kalnins, and W. Miller, Jr.  Tensor products of qsuperalgebras
and qseries identities. I

J. F. van Diejen and J. V. Stokman  qRacah 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
qorthogonal polynomials

P. G. A. Floris  Addition theorems for spherical polynomials on a family
of quantum spheres

F. A. Grünbaum and L. Haine  On a qanalogue of the string
equation and a generalization of the classical orthogonal polynomials

M. E. H. Ismail, D. R. Masson, and S. K. Suslov  The qBessel
function on a qquadratic grid

D. Kim and D. Stanton  Three statistics on lattice paths

A. N. Kirillov  Quantum Grothendieck polynomials

A. N. Kirillov and M. Noumi  qdifference raising operators for
Macdonald polynomials and the integrality of transition coefficients

B. A. Kupershmidt  Great powers of qcalculus

V. Spiridonov  qspecial functions: Differentialdifference equations,
roots of unity, and all that

A. Strasburger  On algebras of creation and annihilation operators
Details:

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: CRM Proceedings & Lecture Notes, ISSN: 10658580

Volume: 22

Publication Year: 1999

ISBN: 0821820265

Paging: 276 pp.

Binding: Softcover

List Price: $79

Institutional Member Price: $63

Individual Member Price: $47

Order Code: CRMP/22