与$D_n^{(1)}$ -晶体$B^{2,s}$相关的孤子元胞自动机
Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$
摘要：
铁磁区的可解顶点模型产生了孤立子元胞自动机，它是一个离散的动力系统，其中位置变量取有限集中的值。研究了与$U_q(D_n^{(1)})$ -完全晶体$B^{2,s}$相关的一类孤子元胞自动机的散射。我们计算组合$R$矩阵的所有元素的$B^{2,s} \otimes B^{2,1}$。特别是，我们表明，我们的孤子元胞自动机的散射规则可以识别与组合$R$矩阵$U_q(A_1^{(1)}) \oplus U_q(D_{n-2}^{(1)})$ -晶体。
英文摘要：
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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