A combinatorial model for crystals of Kac-Moody algebras
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- by Cristian Lenart and Alexander Postnikov PDF
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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.References
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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
- MR Author ID: 259436
- Email: lenart@albany.edu
- Alexander Postnikov
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Email: apost@math.mit.edu
- 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 - © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 4349-4381
- MSC (2000): Primary 17B67; Secondary 22E46, 20G42
- DOI: https://doi.org/10.1090/S0002-9947-08-04419-X
- MathSciNet review: 2395176