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

SIGMA 6 (2010), 023, 14 pages      arXiv:0911.3562      https://doi.org/10.3842/SIGMA.2010.023
Contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems”

Epsilon Systems on Geometric Crystals of Type An

Toshiki Nakashima
Department of Mathematics, Sophia University, 102-8554, Chiyoda-ku, Tokyo, Japan

Received September 14, 2009, in final form January 28, 2010; Published online March 19, 2010

Abstract
We introduce an epsilon system on a geometric crystal of type An, which is a certain set of rational functions with some nice properties. We shall show that it is equipped with a product structure and that it is invariant under the action of tropical R maps.

Key words: geometric crystal; epsilon system; tropical R map.

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