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.

LaTeX2e, 20 pages

References in corpus (7)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Soliton Cellular Automata Associated With Crystal Bases
• Energy Functions in Box Ball Systems
• Geometric Crystal and Tropical R for D^(1)_n
• Simple Algorithm for Factorized Dynamics of g_n-Automaton
• Factorization of Combinatorial R matrices and Associated Cellular Automata
• Tropical R and Tau Functions

Cited by in corpus (6)

• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Soliton cellular automaton associated with $G_2^{(1)}$ crystal base
• A uniform approach to soliton cellular automata using rigged configurations
• Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$
• Analysis of a particle antiparticle description of a soliton cellular automaton