Abstract
A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting end is presented. It extends a box-ball system on an infinite lattice associated with the crystal base of . A commuting family of time evolutions are obtained by adapting the K matrices and the double row construction of transfer matrices in solvable lattice models to a crystal setting. Factorized scattering among the left and the right moving solitons and the boundary reflection rule are determined.
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