Tau functions in combinatorial Bethe ansatz

Details Tau functions in combinatorial Bethe ansatz Tau functions in combinatorial Bethe ansatz

2006-10-17

arxiv.org/abs/math/0610505v2

Nucl.Phys.B786:207-266,2007

Mathematics

Quantum Algebra

52 pages

Scientific paper

10.1016/j.nuclphysb.2007.06.007

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.

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