Special Issue on Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems

The Guest Editors for this special issue are

Nalini Joshi (University of Sydney, Australia)
Erik Koelink (Radboud University Nijmegen, The Netherlands)
Tom Koornwinder (University of Amsterdam, The Netherlands)
Masatoshi Noumi (Kobe University, Japan)
Simon Ruijsenaars (University of Leeds and Loughborough University, UK)
Fedor Smirnov (Université Paris 6, France)
Jasper Stokman (University of Amsterdam, The Netherlands)

Since decades there has been a fruitful interplay between special functions, representation theory and mathematical physics. The special issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems” highlights some of the current developments at these crossroads. Four papers deal with the relation between hypergeometric functions and harmonic analysis on quantum groups, five with the relation between special functions and quantum many-body systems. Other topics covered in this issue are Painlevé equations (four papers) and correlation functions in integrable quantum field theories (one paper).

The issue contains 14 papers with the total of 380 pages.

We thank the authors of the papers for their interesting contributions. We are grateful to the numerous referees for their help in evaluating the manuscripts.

Papers in this Issue:

A Relativistic Conical Function and its Whittaker Limits

Simon Ruijsenaars
SIGMA 7 (2011), 101, 54 pages   [ abs   pdf ]

An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)

Eric M. Rains
SIGMA 7 (2011), 088, 24 pages   [ abs   pdf ]

Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

Martijn Caspers
SIGMA 7 (2011), 087, 39 pages   [ abs   pdf ]

Harmonic Analysis on Quantum Complex Hyperbolic Spaces

Olga Bershtein and Yevgen Kolisnyk
SIGMA 7 (2011), 078, 19 pages   [ abs   pdf ]

Quantum Analogs of Tensor Product Representations of su(1,1)

Wolter Groenevelt
SIGMA 7 (2011), 077, 17 pages   [ abs   pdf ]

The Universal Askey-Wilson Algebra

Paul Terwilliger
SIGMA 7 (2011), 069, 24 pages   [ abs   pdf ]

Recurrence Coefficients of a New Generalization of the Meixner Polynomials

Galina Filipuk and Walter Van Assche
SIGMA 7 (2011), 068, 11 pages   [ abs   pdf ]

On Algebraically Integrable Differential Operators on an Elliptic Curve

Pavel Etingof and Eric Rains
SIGMA 7 (2011), 062, 19 pages   [ abs   pdf ]

Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type A₆⁽¹⁾

Mikio Murata
SIGMA 7 (2011), 059, 15 pages   [ abs   pdf ]

Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere

Ernie G. Kalnins, Willard Miller Jr. and Sarah Post
SIGMA 7 (2011), 051, 26 pages   [ abs   pdf ]

The Fourier Transform on Quantum Euclidean Space

Kevin Coulembier
SIGMA 7 (2011), 047, 30 pages   [ abs   pdf ]

Quantum Integrable Model of an Arrangement of Hyperplanes

Alexander Varchenko
SIGMA 7 (2011), 032, 55 pages   [ abs   pdf ]

Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

Hermann Boos
SIGMA 7 (2011), 007, 36 pages   [ abs   pdf ]

A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function _n+1F_n

Takao Suzuki
SIGMA 6 (2010), 078, 11 pages   [ abs   pdf ]