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2007 Nakajima monomials and crystals for special linear Lie algebras
Hyeonmi Lee
Nagoya Math. J. 188: 31-57 (2007).

Abstract

Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystals $\mathcal{B}(\lambda)$. The monomial set can be extended so that it contains crystal $\mathcal{B}(\infty)$ in addition to $\mathcal{B}(\lambda)$. We present explicit descriptions of the crystals $\mathcal{B}(\infty)$ and $\mathcal{B}(\lambda)$ 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 $\mathcal{B}(\infty)$ and $\mathcal{B}(\lambda)$.

Citation

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Hyeonmi Lee. "Nakajima monomials and crystals for special linear Lie algebras." Nagoya Math. J. 188 31 - 57, 2007.

Information

Published: 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1151.17007
MathSciNet: MR2371768

Subjects:
Primary: 17B37 , 20G05

Rights: Copyright © 2007 Editorial Board, Nagoya Mathematical Journal

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Vol.188 • 2007
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