Scattering rules in soliton cellular automata associated with crystal bases

Details Scattering rules in soliton cellular automata associated with crystal bases Scattering rules in soliton cellular automata associated with crystal bases

2000-07-28

arxiv.org/abs/math/0007175v2

Contemp. Math. 297 (2002) 151-182

Mathematics

Quantum Algebra

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

Scientific paper

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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