Nagoya Mathematical Journal

Level 0 monomial crystals

David Hernandez and Hiraku Nakajima

Full-text: Open access

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.

Article information

Source
Nagoya Math. J. Volume 184 (2006), 85-153.

Dates
First available in Project Euclid: 26 December 2006

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1167159343

Mathematical Reviews number (MathSciNet)
MR2285232

Zentralblatt MATH identifier
05154980

Subjects
Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65]

Citation

Hernandez, David; Nakajima, Hiraku. Level 0 monomial crystals. Nagoya Math. J. 184 (2006), 85--153. http://projecteuclid.org/euclid.nmj/1167159343.


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