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Level 0 Monomial Crystals

Published online by Cambridge University Press:  11 January 2016

David Hernandez  and
Hiraku Nakajima
David Hernandez
Affiliation:
CNRS - UMR 8100: Laboratoire de Mathématiques de Versailles45 avenue des Etats-Unis, Bat. Fermat, 78035 VersaillesFrancehernandez@math.cnrs.fr
Hiraku Nakajima
Affiliation:
Department of MathematicsKyoto UniversityKyoto, 606-8502Japannakajima@math.kyoto-u.ac.jp
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Abstract

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We study the monomial crystal defined by the second author. We show that each component of the monomial crystal can be embedded into a crystal of an extremal weight module introduced by Kashiwara. And we determine all monomials appearing in the components corresponding to all level 0 fundamental representations of quantum affine algebras except for some nodes of . Thus we obtain explicit descriptions of the crystals in these examples. We also give those for the corresponding finite dimensional representations. For classical types, we give them in terms of tableaux. For exceptional types, we list up all monomials.

Keywords

17B3717B65
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 184 , 2006 , pp. 85 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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