# $A n^{(1)}$-Geometric Crystal corresponding to Dynkin index $i=2$ and its ultra-discretization

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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 pro

Author: Kailash C. Misra; Toshiki Nakashima

Source: https://archive.org/