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Affine geometric crystals and limit of perfect crystals

Author(s): Masaki Kashiwara; Toshiki Nakashima; Masato Okado
Journal: Trans. Amer. Math. Soc. 360 (2008), 3645-3686.
MSC (2000): Primary 17B37, 17B67; Secondary 22E65, 14M15
Posted: February 13, 2008
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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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Additional Information:

Masaki Kashiwara
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kitashiwakawa, Sakyo-ku, Kyoto 606, Japan
Email: masaki@kurims.kyoto-u.ac.jp

Toshiki Nakashima
Affiliation: Department of Mathematics, Sophia University, Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan
Email: toshiki@mm.sophia.ac.jp

Masato Okado
Affiliation: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Email: okado@sigmath.es.osaka-u.ac.jp

DOI: 10.1090/S0002-9947-08-04341-9
PII: S 0002-9947(08)04341-9
Received by editor(s): December 29, 2005
Received by editor(s) in revised form: May 11, 2006
Posted: February 13, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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