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Nakajima Monomials and Crystals for Special Linear Lie Algebras

Published online by Cambridge University Press:  11 January 2016

Hyeonmi Lee
Hyeonmi Lee*
Affiliation:
Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-722, Korea, hmlee@kias.re.kr
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Abstract

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Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystals B(λ). The monomial set can be extended so that it contains crystal B(∞) in addition to B(λ). We present explicit descriptions of the crystals B(∞) and B(λ) over special linear Lie algebras in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystals B(∞) and B(λ).

Keywords

17B3720G05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 188 , December 2007 , pp. 31 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

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