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This https://arxiv.org/abs/2404.06321 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On $C_n^{(1)}$-Geometric Crystal and its Ultradiscretization
Let $\ge$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$ and $\ge^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i \in I \setminus \{0\}$ the affine Lie algebra $\ge$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a certain coherent family of perfect crystals for the Langland dual $\ge^L$. In this paper we construct positive geometric crystals for $\mathcal{V}(C_n^{(1)})$ in the level zero fundamental spin…

On $C_n^{(1)}$-Geometric Crystal and its Ultradiscretization
Erica S. Dinkins, Kailash C. Misra
https://arxiv.org/abs/2404.06321 https://

On $C_n^{(1)}$-Geometric Crystal and its Ultradiscretization
Let $\ge$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$ and $\ge^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i \in I \setminus \{0\}$ the affine Lie algebra $\ge$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a certain coherent family of perfect crystals for the Langland dual $\ge^L$. In this paper we construct positive geometric crystals for $\mathcal{V}(C_n^{(1)})$ in the level zero fundamental spin…