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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Affine geometric crystals and limit of perfect crystals


Authors: Masaki Kashiwara, Toshiki Nakashima and Masato Okado
Journal: Trans. Amer. Math. Soc. 360 (2008), 3645-3686
MSC (2000): Primary 17B37, 17B67; Secondary 22E65, 14M15
Published electronically: February 13, 2008
MathSciNet review: 2386241
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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: http://dx.doi.org/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
Published electronically: February 13, 2008
Article copyright: © Copyright 2008 American Mathematical Society