Analysis of a particle antiparticle description of a soliton cellular automaton

TL;DR

This paper derives a formula describing the dynamics of an integrable cellular automaton related to crystal bases and affine Lie algebras, incorporating particles and antiparticles, extending box-ball systems.

Contribution

It provides a new derivation of the automaton's dynamics from combinatorial R-matrix formulas linked to geometric crystals, connecting integrable systems and algebraic structures.

Findings

Derived a formula for automaton dynamics involving particles and antiparticles

Connected the automaton to type D affine Lie algebra and box-ball systems

Linked combinatorial R-matrix with cellular automaton evolution

Abstract

We present a derivation of a formula that gives dynamics of an integrable cellular automaton associated with crystal bases. This automaton is related to type D affine Lie algebra and contains usual box-ball systems as a special case. The dynamics is described by means of such objects as carriers, particles, and antiparticles. We derive it from an analysis of a recently obtained formula of the combinatorial R (an intertwiner between tensor products of crystals) that was found in a study of geometric crystals.