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

 

On the combinatorics of crystal graphs, II. The crystal commutor


Author: Cristian Lenart
Journal: Proc. Amer. Math. Soc. 136 (2008), 825-837
MSC (2000): Primary 20G42; Secondary 17B10, 22E46
Published electronically: November 30, 2007
MathSciNet review: 2361854
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Abstract: We present an explicit combinatorial realization of the commutor in the category of crystals which was first studied by Henriques and Kamnitzer. Our realization is based on certain local moves defined by van Leeuwen.


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Additional Information

Cristian Lenart
Affiliation: Department of Mathematics and Statistics, State University of New York at Albany, Albany, New York 12222
Email: lenart@albany.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09244-1
PII: S 0002-9939(07)09244-1
Keywords: Crystals, root operators, coboundary category, commutor, Lusztig's involution, van Leeuwen's jeu de taquin.
Received by editor(s): February 16, 2007
Published electronically: November 30, 2007
Additional Notes: The author was supported by National Science Foundation grant DMS-0403029
Communicated by: Jim Haglund
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.