Separation of colour degree of freedom from dynamics in a soliton cellular automaton
Taichiro Takagi · Journal of Physics A Mathematical and General · 2005
We present an algorithm to reduce the coloured box–ball system, a one-dimensional integrable cellular automaton described by motions of several colours (kinds) 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.