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29 March 2024
 
  » arxiv » nlin.CG/0310002

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Factorization, reduction and embedding in integrable cellular automata
A. Kuniba ; T. Takagi ; A. Takenouchi ;
Date 3 Oct 2003
Journal J. of Phys. A: Math. Gen. 37 (2004) 1691-1709
Subject Cellular Automata and Lattice Gases; Exactly Solvable and Integrable Systems; Quantum Algebra | nlin.CG math.QA nlin.SI
AbstractFactorized 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.
Source arXiv, nlin.CG/0310002
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