Soliton Cellular Automata Associated With Crystal Bases
Abstract
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U'q(n). They have solitons labeled by crystals of the smaller algebra U'q(n-1). We prove stable propagation of one soliton for n = A(2)2n-1, A(2)2n, B(1)n, C(1)n, D(1)n and D(2)n+1. For n = 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.
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