Level 0 monomial crystals
David Hernandez and Hiraku Nakajima
Source: Nagoya Math. J. Volume 184
(2006), 85-153.
Abstract
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 $E_{6}^{(2)}$, $E_{7}^{(1)}$, $E_{8}^{(1)}$. 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.
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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1167159343
Mathematical Reviews number (MathSciNet): MR2285232
Zentralblatt MATH identifier: 05154980
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