arXiv:math/9912209math.QA
The A^{(1)}_M automata related to crystals of symmetric tensors
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Abstract
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.
That's the most beautiful chart I've ever seen. I found: The A^(1)_M automata related to crystals of symmetric tensors G. Hatayama, K. Hikami, R. Inoue, A. Kuniba, T. Takagi, T. Tokihiro J.Math.Phys. 42 (2001) 274 [Open paper's DOI page in a new tab] arXiv: math/9912209…
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