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Affine Geometric Crystals and Limit of Perfect Crystals

Masaki Kashiwara, Toshiki Nakashima, Masato Okado

math.QAarXiv:math/0512657

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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