Simple algorithm for factorized dynamics of the $\frak{g}_n$-automaton
Goro Hatayama, Atsuo Kuniba, Taichiro Takagi ยท Journal of Physics A Mathematical and General ยท 2001
We present an elementary algorithm for the dynamics of recently introduced soliton cellular automata associated with quantum affine algebra U q (๐ค n ) at q = 0. For ๐ค n = A (1) n , the rule reproduces the ball-moving algorithm in Takahashi-Satsuma's box-ball system. For non-exceptional ๐ค 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 or crystal basis theory.