Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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.

The Guest Editors        

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+1Fn
Takao Suzuki
SIGMA 6 (2010), 078, 11 pages   [ abs   pdf ]

The poster of the issue is available in A4 format and A3 format.

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