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

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.

37 pages. arXiv admin note: text overlap with arXiv:1109.2836

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Cited by in corpus (2)

• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• A uniform approach to soliton cellular automata using rigged configurations