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

 

Generalized Young walls and crystal bases for quantum affine algebra of type $ A$


Authors: Jeong-Ah Kim and Dong-Uy Shin
Journal: Proc. Amer. Math. Soc. 138 (2010), 3877-3889
MSC (2010): Primary 17B37, 81R50
Published electronically: June 9, 2010
MathSciNet review: 2679610
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Abstract: We give a new realization of the crystal $ B(\infty)$ of $ U_q^{-}(A_n^{(1)})$ using generalized Young walls, a modified notion of Young walls of type $ A_n^{(1)}$. Moreover, by the fact that the irreducible highest weight crystal $ B(\lambda)$ lies in the crystal $ B(\infty)\otimes R_{\lambda}$, we construct the crystal $ B(\lambda)$ using generalized Young walls.


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Additional Information

Jeong-Ah Kim
Affiliation: Department of Mathematics, University of Seoul, Seoul, 130-743, Korea
Email: jakim@uos.ac.kr

Dong-Uy Shin
Affiliation: Department of Mathematics Education, Hanyang University, Seoul 133-791, Korea
Email: dushin@hanyang.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10428-8
PII: S 0002-9939(2010)10428-8
Received by editor(s): August 12, 2009
Received by editor(s) in revised form: January 20, 2010, and February 3, 2010
Published electronically: June 9, 2010
Additional Notes: This work was supported by the research fund of Hanyang University (HY-2009-O)
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.