$A_n^{(1)}$ -对应于Dynkin指数$i=2$的几何晶体及其超离散化
$A_n^{(1)}$-Geometric Crystal corresponding to Dynkin index $i=2$ and its ultra-discretization
摘要：
设$g$是一个具有指标集$I = \{0, 1, 2,..., n\}$的仿射李代数，$g^L$是它的Langlands对偶.证明了对每个$i \in I \setminus \{0\}$，仿射李代数$g$都有一个正几何晶体，其超离散化同构于$g^L$的某个相干完美晶体族的极限.我们证明了这个猜想$i=2$和$g = A_n^{(1)}$。
英文摘要：
Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2,..., n\}$ and $g^L$ be its Langlands dual. It is conjectured that for each $i \in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for $g^L$. We prove this conjecture for $i=2$ and $g = A_n^{(1)}$.
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