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 U_q(g_n) for non exceptional series g_n = 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 U_q(g_{n-1}). Two-soliton scattering rule is identified with the combinatorial R of U_q(g_{n-1})-crystals, and the multi-soliton scattering is shown to factorize into the two-body ones.

31pages, LaTeX2e, no figure. For proceedings of Infinite-Dimensional Lie Theory and Conformal Field Theory. Some minor points corrected