Periodic cellular automata and Bethe ansatz
Atsuo Kuniba, Akira Takenouchi · arXiv (Cornell University) · 2005
We review and generalize the recent progress in a soliton cellular automaton known as the periodic box-ball system. It has the extended affine Weyl group symmetry and admits the commuting transfer matrix method and the Bethe ansatz at q=0. Explicit formulas are proposed for the dynamical period and the number of states characterized by conserved quantities.