Affine geometric crystals and limit of perfect crystals

Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato

doi:10.1090/S0002-9947-08-04341-9

Affine geometric crystals and limit of perfect crystals
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by Masaki Kashiwara, Toshiki Nakashima and Masato Okado PDF

Trans. Amer. Math. Soc. 360 (2008), 3645-3686 Request permission

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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