Factorization, reduction and embedding in integrable cellular automata
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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