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