A Combinatorial Model for Crystals of Kac-Moody Algebras

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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.
28 pages, 2 figures

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Representation Theory, Combinatorics, 17B67; 22E46, 20G42

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http://salesiana.dossiersoluciones.com/handle/123456789/101065

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502147
 http://arxiv.org/abs/math/0502147

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arXiv