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

Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems” (March 30 − April 3, 2009, University of Glasgow, UK)

The Guest Editors for this special issue are

Christian Korff (University of Glasgow, UK)
Masato Okado (Osaka University, Japan)
Wolfgang K. Schief (Technische Universität Berlin, Germany)
Tetsuji Tokihiro (The University of Tokyo, Japan)

The satellite workshop Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems (March 30 − April 3, 2009) was part of the Isaac Newton Institute Programme on Discrete Integrable Systems (January 19 − July 3, 2009). It brought together different communities of researchers working on classical and quantum aspects of integrable systems as well as experts on combinatorial representation theory and crystals and this interdisciplinary aspect is reflected in this proceedings volume.

On behalf of the other organisers, Claire Gilson and Jon Nimmo, I would like to express our gratitude to the participants of the workshop, the contributing authors to this volume, the guest editors (Professors Masato Okado, Wolfgang Schief and Tetsuji Tokihiro) and the organisers of the Discrete Integrable Systems programme as well as the support staff of the Isaac Newton Institute.

Christian Korff         Glasgow, April 9, 2010        

Papers in this Issue:

On Quadrirational Yang-Baxter Maps
V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas and A.P. Veselov
SIGMA 6 (2010), 033,  9 pages   [ abs   pdf   ps ]
Yang-Baxter Maps from the Discrete BKP Equation
Saburo Kakei, Jonathan J.C. Nimmo and Ralph Willox
SIGMA 6 (2010), 028, 11 pages   [ abs   pdf   ps ]
Level Set Structure of an Integrable Cellular Automaton
Taichiro Takagi
SIGMA 6 (2010), 027, 18 pages   [ abs   pdf   ps ]
Epsilon Systems on Geometric Crystals of Type An
Toshiki Nakashima
SIGMA 6 (2010), 023, 14 pages   [ abs   pdf   ps ]
Zero Action on Perfect Crystals for Uq(G2(1))
Kailash C. Misra, Mahathir Mohamad and Masato Okado
SIGMA 6 (2010), 022, 12 pages   [ abs   pdf   ps ]
Q-system Cluster Algebras, Paths and Total Positivity
Philippe Di Francesco and Rinat Kedem
SIGMA 6 (2010), 014, 36 pages   [ abs   pdf   ps ]
Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for An(1)
Atsuo Kuniba and Taichiro Takagi
SIGMA 6 (2010), 013, 52 pages   [ abs   pdf   ps ]

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