Algebraic Methods and
q-Special 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 representation-theoretic methods, combinatorics of symmetric functions,
root systems, and the connections with integrable systems.
Contents
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F. Bergeron and A. M. Garsia -- Science fiction and Macdonald's polynomials
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R. Chouikha -- On the expansion of elliptic functions and applications
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D. V. Chudnovsky and G. V. Chudnovsky -- Generalized hypergeometric functions-Classification
of identities and explicit rational approximations
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W. S. Chung, E. G. Kalnins, and W. Miller, Jr. -- Tensor products of q-superalgebras
and q-series identities. I
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J. F. van Diejen and J. V. Stokman -- q-Racah polynomials for BC
type root systems
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C. F. Dunkl -- Intertwining operators of type B_N
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R. Floreanini, J. LeTourneux, and L. Vinet -- Symmetries and continuous
q-orthogonal polynomials
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P. G. A. Floris -- Addition theorems for spherical polynomials on a family
of quantum spheres
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F. A. Grünbaum and L. Haine -- On a q-analogue of the string
equation and a generalization of the classical orthogonal polynomials
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M. E. H. Ismail, D. R. Masson, and S. K. Suslov -- The q-Bessel
function on a q-quadratic grid
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D. Kim and D. Stanton -- Three statistics on lattice paths
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A. N. Kirillov -- Quantum Grothendieck polynomials
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A. N. Kirillov and M. Noumi -- q-difference raising operators for
Macdonald polynomials and the integrality of transition coefficients
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B. A. Kupershmidt -- Great powers of q-calculus
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V. Spiridonov -- q-special functions: Differential-difference equations,
roots of unity, and all that
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A. Strasburger -- On algebras of creation and annihilation operators
Details:
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Publisher: American Mathematical Society
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Distributor: American Mathematical Society
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Series: CRM Proceedings & Lecture Notes, ISSN: 1065-8580
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Volume: 22
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Publication Year: 1999
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ISBN: 0-8218-2026-5
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Paging: 276 pp.
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Binding: Softcover
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List Price: $79
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Institutional Member Price: $63
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Individual Member Price: $47
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Order Code: CRMP/22