Epsilon Systems on Geometric Crystals of Type An

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Author: Nakashima, T.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146309
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Epsilon Systems on Geometric Crystals of Type An / T. Nakashima // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 12 назв. — англ.

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.