Combinatorial Bethe ansatz and generalized periodic box-ball system

Details Combinatorial Bethe ansatz and generalized periodic box-ball system Combinatorial Bethe ansatz and generalized periodic box-ball system

2007-08-24

arxiv.org/abs/0708.3287v2

Rev.Math.Phys.20:493-527,2008

Mathematics

Quantum Algebra

27 pages

Scientific paper

10.1142/S0129055X08003365

We reformulate the Kerov-Kirillov-Reshetikhin (KKR) map in the combinatorial Bethe ansatz from paths to rigged configurations by introducing local energy distribution in crystal base theory. Combined with an earlier result on the inverse map, it completes the crystal interpretation of the KKR bijection for U_q(\hat{sl}_2). As an application, we solve an integrable cellular automaton, a higher spin generalization of the periodic box-ball system, by an inverse scattering method and obtain the solution of the initial value problem in terms of the ultradiscrete Riemann theta function.

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