SIGMA 6 (2010), 033, 9 pages      arXiv:0911.2895      https://doi.org/10.3842/SIGMA.2010.033
Contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems”

On Quadrirational Yang-Baxter Maps

V.G. Papageorgiou ^a, Yu.B. Suris ^b, A.G. Tongas ^c and A.P. Veselov ^{d, e
a)} Department of Mathematics, University of Patras, 26 500 Patras, Greece
^b) Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
^c) Department of Applied Mathematics, University of Crete, 714 09 Heraklion, Greece
^d) School of Mathematics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
^e) Moscow State University, Moscow 119899, Russia

Received November 15, 2009, in final form March 26, 2010; Published online April 16, 2010

Abstract
We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.

Key words: Yang-Baxter maps; birational maps; integrability.

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References

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