Simple Algorithm for Factorized Dynamics of g_n-Automaton

Abstract

We present an elementary algorithm for the dynamics of recently introduced soliton cellular automata associated with quantum affine algebra U_q(g_n) at q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in Takahashi-Satsuma's box-ball system. For non-exceptional g_n other than A^{(1)}_n, it is described as a motion of particles and anti-particles which undergo pair-annihilation and creation through a neutral bound state. The algorithm is formulated without using representation theory nor crystal basis theory.

LaTex2e 9 pages, no figure. For proceedings of SIDE IV conference

References in corpus (3)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Soliton Cellular Automata Associated With Crystal Bases
• Factorization of Combinatorial R matrices and Associated Cellular Automata

Cited by in corpus (9)

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Inversible Max-Plus Algebras and Integrable systems
• Rigged Configurations and Kashiwara Operators
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Tropical R and Tau Functions
• Factorization, reduction and embedding in integrable cellular automata
• A uniform approach to soliton cellular automata using rigged configurations
• A Quantization of Box-Ball Systems
• Analysis of a particle antiparticle description of a soliton cellular automaton