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arXiv · 1209.4558

Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$

Kailash C. Misra·Evan A. Wilson
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Abstract

A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the $U_q(D_n^{(1)})$-perfect crystal $B^{2,s}$. We calculate the combinatorial $R$ matrix for all elements of $B^{2,s} \otimes B^{2,1}$. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial $R$ matrix for $U_q(A_1^{(1)}) \oplus U_q(D_{n-2}^{(1)})$-crystals.

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Kailash C. Misra, Evan A. Wilson. 2012-09-20. Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$. https://doi.org/10.1063/1.4801448

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