Separation of colour degree of freedom from dynamics in a soliton cellular automaton
arXiv:math-ph/0411013 · doi:10.1088/0305-4470/38/9/009
Abstract
We present an algorithm to reduce the coloured box-ball system, a one dimensional integrable cellular automaton described by motions of several colour (kind) of balls, into a simpler monochrome system. This algorithm extracts the colour degree of freedom of the automaton as a word which turns out to be a conserved quantity of this dynamical system. It is based on the theory of crystal basis and in particular on the tensor products of sl_n crystals of symmetric and anti-symmetric tensor representations.
19 pages