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.References
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Additional Information
- Masaki Kashiwara
- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kitashiwakawa, Sakyo-ku, Kyoto 606, Japan
- MR Author ID: 98845
- 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
- Received by editor(s): December 29, 2005
- Received by editor(s) in revised form: May 11, 2006
- Published electronically: February 13, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 3645-3686
- MSC (2000): Primary 17B37, 17B67; Secondary 22E65, 14M15
- DOI: https://doi.org/10.1090/S0002-9947-08-04341-9
- MathSciNet review: 2386241