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Affine Geometric Crystals and Limit of Perfect Crystals

Masaki Kashiwara·Toshiki Nakashima·Masato Okado
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Abstract

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect crystals of the Langlands dual affine Lie algebra.

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Masaki Kashiwara, Toshiki Nakashima, Masato Okado. 2005-12-30. Affine Geometric Crystals and Limit of Perfect Crystals. https://arxiv.org/abs/math/0512657

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