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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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