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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The crystal $ \mathcal{B}(\infty)$ and extended Nakajima monomials


Author: Hyeonmi Lee
Journal: Proc. Amer. Math. Soc. 137 (2009), 1915-1924
MSC (2000): Primary 20G05; Secondary 17B37, 81R50
Published electronically: January 26, 2009
MathSciNet review: 2480271
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Abstract: We construct the set of extended Nakajima monomials containing monomials realizing the irreducible highest weight crystals, introduced by Nakajima. We present explicit descriptions of a crystal $ \mathcal{B}_{\infty}$ and the crystal $ \mathcal{B}(\infty)$ in this language for the case $ A_n^{(1)}$.


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Additional Information

Hyeonmi Lee
Affiliation: Department of Mathematics, Hanyang University, Seoul 133-791, Korea
Email: hyeonmi@hanyang.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09834-7
PII: S 0002-9939(09)09834-7
Keywords: Crystal, extended Nakajima monomial
Received by editor(s): June 23, 2008
Published electronically: January 26, 2009
Additional Notes: This work was supported by the research fund of KIAS
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2009 American Mathematical Society