Soliton Cellular Automata Associated With Crystal Bases

Details Soliton Cellular Automata Associated With Crystal Bases Soliton Cellular Automata Associated With Crystal Bases

1999-07-27

arxiv.org/abs/solv-int/9907020v2

Nuclear Physics B577[PM](2000) 619-645

Mathematics

Quantum Algebra

29 pages, 1 figure, LaTeX2e

Scientific paper

10.1016/S0550-3213(00)00105-X

We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U'_q(\hat{\geh}_n). They have solitons labeled by crystals of the smaller algebra U'_q(\hat{\geh}_{n-1}). We prove stable propagation of one soliton for \hat{\geh}_n = A^{(2)}_{2n-1}, A^{(2)}_{2n}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}. For \gh_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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