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

Taichiro Takagi

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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 sln crystals of symmetric and anti-symmetric tensor representations.


PACS

05.45.Yv Solitons

02.30.Ik Integrable systems

02.10.Ud Linear algebra

MSC

15A69 Multilinear algebra, tensor products

37K40 Soliton theory, asymptotic behavior of solutions

37B15 Cellular automata

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 9 (4 March 2005)

Received 8 November 2004, in final form 30 December 2004

Published 16 February 2005



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