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Scattering rules in soliton cellular automata associated with crystal bases

G. Hatayama·A. Kuniba·M. Okado·T. Takagi·Y. Yamada
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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.

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G. Hatayama, A. Kuniba, M. Okado, T. Takagi, Y. Yamada. 2001-01-09. Scattering rules in soliton cellular automata associated with crystal bases. https://arxiv.org/abs/math/0007175

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