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Factorization, reduction and embedding in integrable cellular automata

A. Kuniba·T. Takagi·A. Takenouchi
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Abstract

Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and all the other automata associated with the crystal bases of non-exceptional affine Lie algebras. The results extend the earlier ones to higher representations by a certain reduction and to a wider class of boundary conditions.

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A. Kuniba, T. Takagi, A. Takenouchi. 2003-10-03. Factorization, reduction and embedding in integrable cellular automata. https://doi.org/10.1088/0305-4470%2F37%2F5%2F015

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