Soliton cellular automata associated with crystal bases Original Research Article

We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U′q(ĝn). They have solitons labeled by crystals of the smaller algebra U′q(ĝn−1). We prove stable propagation of one soliton for ĝn=A(2)2n−1,A(2)2n,B(1)n,C(1)n,D(1)n and D(2)n+1. For ĝn=C(1)n, we also prove that the scattering matrices of two solitons coincide with the combinatorial R matrices of U′q(C(1)n−1)-crystals.