The A^{(1)}_M automata related to crystals of symmetric tensors

Details The A^{(1)}_M automata related to crystals of symmetric tensors The A^{(1)}_M automata related to crystals of symmetric tensors

1999-12-27

arxiv.org/abs/math/9912209v1

J. Math. Phys. 42(2001) 274-308

Mathematics

Quantum Algebra

45 pages, latex2e, 2 figures

Scientific paper

10.1063/1.1322077

A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U'_q(A^{(1)}_M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering matrices of two solitons coincide with the combinatorial R matrices of U'_q(A^{(1)}_{M-1}). A piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete KP equation. A class of N soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter.

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