On $C_n^{(1)}$-Geometric Crystal and its Ultradiscretization

Erica S. Dinkins, Kailash C. Misra

Let $\mathfrak{g}$ be an affine Lie algebra with index set $I=\{0,1,2,\cdots ,n\}$ and ${\mathfrak{g}}^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i…