Ultra-discretization of the G(1)2-Geometric Crystals to the D(3)4-Perfect Crystals
Abstract
We obtain the affirmative answer to the conjecture in [15]. More precisely, let X be the affine geometric crystal of type G(1)2 in [15] and UD(X,T,θ) a ultra-discretization of X with respect to a certain positive structure θ. Then we show that UD(X,T,θ) is isomorphic to the limit of coherent family of perfect crystals of type D(3)4 in [7].
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