Factorization, reduction and embedding in integrable cellular automata

Details Factorization, reduction and embedding in integrable cellular automata Factorization, reduction and embedding in integrable cellular automata

2003-10-03

arxiv.org/abs/nlin/0310002v1

J. of Phys. A: Math. Gen. 37 (2004) 1691-1709

Nonlinear Sciences

Cellular Automata and Lattice Gases

LaTeX2e, 20 pages

Scientific paper

10.1088/0305-4470/37/5/015

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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