Ultra-discretization of the D_4^3-Geometric Crystals to the G_2^1-Perfect Crystals

Details Ultra-discretization of the D_4^3-Geometric Crystals to the G_2^1-Perfect Crystals Ultra-discretization of the D_4^3-Geometric Crystals to the G_2^1-Perfect Crystals

2010-03-05

arxiv.org/abs/1003.1242v1

Mathematics

Quantum Algebra

Scientific paper

Let g be an affine Lie algebra and g^L 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 g^L. We prove that the ultra-discretization of the positive geometric crystal for g = D_4^3 given by Igarashi and Nakashima is isomorphic to the limit of the coherent family of perfect crystals for g^L= G_2^1 constructed recently by Misra, Mohamad and Okado.

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