Tropical R and Tau Functions
Quantum Algebra
2009-11-10 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Tropical R is the birational map that intertwines products of geometric crystals and satisfies the Yang-Baxter equation. We show that the D^{(1)}_n tropical R introduced by the authors and its reduction to A^{(2)}_{2n-1} and C^{(1)}_n are equivalent to a system of bilinear difference equations of Hirota type. Associated tropical vertex models admit solutions in terms of tau functions of the BKP and DKP hierarchies.
Keywords
Cite
@article{arxiv.math/0303088,
title = {Tropical R and Tau Functions},
author = {Atsuo Kuniba and Masato Okado and Taichiro Takagi and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:math/0303088},
year = {2009}
}
Comments
LaTeX2e, 26pages