Tau functions in combinatorial Bethe ansatz
Quantum Algebra
2008-11-26 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead to general N-soliton solutions of the box-ball system.
Keywords
Cite
@article{arxiv.math/0610505,
title = {Tau functions in combinatorial Bethe ansatz},
author = {Atsuo Kuniba and Reiho Sakamoto and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:math/0610505},
year = {2008}
}
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52 pages