Separation of colour degree of freedom from dynamics in a soliton cellular automaton

Details Separation of colour degree of freedom from dynamics in a soliton cellular automaton Separation of colour degree of freedom from dynamics in a soliton cellular automaton

2004-11-04

arxiv.org/abs/math-ph/0411013v1

J. Phys. A: Math. Gen. 38 (2005) 1961-1976

Physics

Mathematical Physics

19 pages

Scientific paper

10.1088/0305-4470/38/9/009

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.

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