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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generalized Young walls and crystal bases for quantum affine algebra of type $A$
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by Jeong-Ah Kim and Dong-Uy Shin PDF
Proc. Amer. Math. Soc. 138 (2010), 3877-3889 Request permission

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
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3877-3889
  • MSC (2010): Primary 17B37, 81R50
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10428-8
  • MathSciNet review: 2679610