论文标题
$ d_6^{（1）} $的超差 - 旋转节点的几何晶体
Ultra-Discretization of $D_6^{(1)}$- Geometric Crystal at the spin node
论文作者
论文摘要
令$ \ mathfrak g $为索引的代数，索引设置$ i = \ {0，1，2，\ cdots，n \} $。 It is conjectured in \cite{KNO} that for each Dynkin node $k \in I \setminus \{0\}$ the affine Lie algebra $\mathfrak g$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a coherent family of perfect crystals for the Langland dual ${\mathfrak g} ^L$.在本文中，我们表明，在自旋节点$ k = 6 $，在\ cite {kmn2}中给出的完美晶体家族形成一个连贯的家族，并表明其极限$ b^{6，\ infty} $是对\ cite a for Aff act的正式criptal for Aff cite {mp}的ultra-discretization {mp} $ d_6^{（1）} $，在这种情况下证明了猜想。
Let $\mathfrak g$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$. It is conjectured in \cite{KNO} that for each Dynkin node $k \in I \setminus \{0\}$ the affine Lie algebra $\mathfrak g$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a coherent family of perfect crystals for the Langland dual ${\mathfrak g} ^L$. In this paper we show that at the spin node $k=6$, the family of perfect crystals given in \cite{KMN2} form a coherent family and show that its limit $B^{6,\infty}$ is isomorphic to the ultra-discretization of the positive geometric crystal we constructed in \cite{MP} for the affine Lie algebra $D_6^{(1)}$ which proves the conjecture in this case.
