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A Combinatorial Model for Crystals of Kac-Moody Algebras

Cristian Lenart·Alexander Postnikov
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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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Cristian Lenart, Alexander Postnikov. 2006-09-01. A Combinatorial Model for Crystals of Kac-Moody Algebras. https://arxiv.org/abs/math/0502147

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