Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B37, 81R50

Retrieve articles in all journals with MSC (2010): 17B37, 81R50

Additional Information

Jeong-Ah Kim
Affiliation: Department of Mathematics, University of Seoul, Seoul, 130-743, Korea

Dong-Uy Shin
Affiliation: Department of Mathematics Education, Hanyang University, Seoul 133-791, Korea

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.