Ultra-discretization of the D43-Geometric Crystals to the G21-Perfect Crystals
Abstract
Let g be an affine Lie algebra and gL be its Langlands dual. It is conjectured that g has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for gL. We prove that the ultra-discretization of the positive geometric crystal for g = D43 given by Igarashi and Nakashima is isomorphic to the limit of the coherent family of perfect crystals for gL= G21 constructed recently by Misra, Mohamad and Okado.
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