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

Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21−25, 2008, MPIM, Bonn, Germany)

The Guest Editors for this special issue are

Masatoshi Noumi (Kobe University, Japan)
Eric M. Rains (California Institute of Technology, USA)
Hjalmar Rosengren (Chalmers University of Technology and University of Gothenburg, Sweden)
Vyacheslav P. Spiridonov (Joint Institute for Nuclear Research, Dubna, Russia)

The present collection includes papers by participants of the workshop ''Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions", held at Max Planck Institute for Mathematics in Bonn July 21−25, 2008. The meeting was a satellite to the 5th European Congress of Mathematics, and a continuation of the workshop ''Elliptic Integrable Systems'' held at RIMS (Kyoto) in November 2004.

The workshop gathered 35 participants from 13 countries. There were 23 lectures, presenting the latest advances on elliptic hypergeometric functions and their relation to integrable systems, Painlevé equations and other fields. A detailed programme can be found at the conference web page.

We would like to thank the Max Planck Institute for Mathematics, the Hausdorff Center for Mathematics, and the 5th European Congress of Mathematics for financial support. We would also like to thank all the authors who have published papers in the issue, as well as the referees for providing constructive reviews.

The Guest Editors        

Papers in this Issue:

Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model
Vladimir Rubtsov, Alexey Silantyev and Dmitri Talalaev
SIGMA 5 (2009), 110, 22 pages   [ abs   pdf   ps ]
Monopoles and Modifications of Bundles over Elliptic Curves
Andrey M. Levin, Mikhail A. Olshanetsky and Andrei V. Zotov
SIGMA 5 (2009), 065, 22 pages   [ abs   pdf   ps ]
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
Fokko J. van de Bult and Eric M. Rains
SIGMA 5 (2009), 059, 31 pages   [ abs   pdf   ps ]
Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
Robin Langer, Michael J. Schlosser and S. Ole Warnaar
SIGMA 5 (2009), 055, 20 pages   [ abs   pdf   ps ]
Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
Yasushi Komori, Masatoshi Noumi and Jun'ichi Shiraishi
SIGMA 5 (2009), 054, 40 pages   [ abs   pdf   ps ]
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case
Simon N.M. Ruijsenaars
SIGMA 5 (2009), 049, 21 pages   [ abs   pdf   ps ]
A Lax Formalism for the Elliptic Difference Painlevé Equation
Yasuhiko Yamada
SIGMA 5 (2009), 042, 15 pages   [ abs   pdf   ps ]
A First Order q-Difference System for the BC1-Type Jackson Integral and Its Applications
Masahiko Ito
SIGMA 5 (2009), 041, 14 pages   [ abs   pdf   ps ]
Middle Convolution and Heun's Equation
Kouichi Takemura
SIGMA 5 (2009), 040, 22 pages   [ abs   pdf   ps ]
Elliptic Hypergeometric Solutions to Elliptic Difference Equations
Alphonse P. Magnus
SIGMA 5 (2009), 038, 12 pages   [ abs   pdf   ps ]
Hypergeometric τ-Functions of the q-Painlevé System of Type E7(1)
Tetsu Masuda
SIGMA 5 (2009), 035, 30 pages   [ abs   pdf   ps ]
Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
Satoshi Tsujimoto and Alexei Zhedanov
SIGMA 5 (2009), 033, 30 pages   [ abs   pdf   ps ]
Differential and Functional Identities for the Elliptic Trilogarithm
Ian A.B. Strachan
SIGMA 5 (2009), 031, 12 pages   [ abs   pdf   ps ]

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