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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A combinatorial model for crystals of Kac-Moody algebras


Authors: Cristian Lenart and Alexander Postnikov
Journal: Trans. Amer. Math. Soc. 360 (2008), 4349-4381
MSC (2000): Primary 17B67; Secondary 22E46, 20G42
Published electronically: February 27, 2008
MathSciNet review: 2395176
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Abstract: We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a Littlewood-Richardson rule for decomposing tensor products of irreducible representations. The new model is based on the notion of a $ \lambda$-chain, which is a chain of positive roots defined by certain interlacing conditions.


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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

Alexander Postnikov
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: apost@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04419-X
PII: S 0002-9947(08)04419-X
Received by editor(s): November 28, 2005
Received by editor(s) in revised form: September 1, 2006
Published electronically: February 27, 2008
Additional Notes: The first author was supported by National Science Foundation grant DMS-0403029 and by SUNY Albany Faculty Research Award 1039703
The second author was supported by National Science Foundation grant DMS-0201494 and by an Alfred P.\ Sloan Foundation research fellowship
Article copyright: © Copyright 2008 American Mathematical Society