Ultra-discretization of the G^(1)_2-Geometric Crystals to the D^(3)_4-Perfect Crystals
Abstract
Description
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].
19 pages
19 pages