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Simple Algorithm for Factorized Dynamics of g_n-Automaton

Goro Hatayama·Atsuo Kuniba·Taichiro Takagi
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Abstract

We present an elementary algorithm for the dynamics of recently introduced soliton cellular automata associated with quantum affine algebra U_q(g_n) at q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in Takahashi-Satsuma's box-ball system. For non-exceptional g_n other than A^{(1)}_n, it is described as a motion of particles and anti-particles which undergo pair-annihilation and creation through a neutral bound state. The algorithm is formulated without using representation theory nor crystal basis theory.

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Goro Hatayama, Atsuo Kuniba, Taichiro Takagi. 2001-03-16. Simple Algorithm for Factorized Dynamics of g_n-Automaton. https://doi.org/10.1088/0305-4470%2F34%2F48%2F331

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