Tropical R and Tau Functions
arXiv:math/0303088 · doi:10.1007/s00220-003-1015-1
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.
LaTeX2e, 26pages
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- Yang-Baxter maps: dynamical point of view
- Factorization, reduction and embedding in integrable cellular automata
- Two-component Yang-Baxter maps and star-triangle relations
- A Quantization of Box-Ball Systems
- Analysis of a particle antiparticle description of a soliton cellular automaton