On Quadrirational Yang-Baxter Maps

Mathematics – Quantum Algebra

Scientific paper

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Proceedings of the workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (Glasgow, March-April 2009)

Scientific paper

10.3842/SIGMA.2010.033

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.

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