Scattering rules in soliton cellular automata associated with crystal bases
Abstract
Solvable vertex models in a ferromagnetic regime give rise to soliton cellular automata at q=0. By means of the crystal base theory, we study a class of such automata associated with the quantum affine algebra Uq(gn) for non exceptional series gn = A(2)2n-1, A(2)2n, B(1)n, C(1)n, D(1)n and D(2)n+1. They possess a commuting family of time evolutions and solitons labeled by crystals of the smaller algebra Uq(gn-1). Two-soliton scattering rule is identified with the combinatorial R of Uq(gn-1)-crystals, and the multi-soliton scattering is shown to factorize into the two-body ones.
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