A combinatorial model for crystals of Kac-Moody algebras

Lenart, Cristian; Postnikov, Alexander

doi:10.1090/S0002-9947-08-04419-X

A combinatorial model for crystals of Kac-Moody algebras
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by Cristian Lenart and Alexander Postnikov PDF

Trans. Amer. Math. Soc. 360 (2008), 4349-4381 Request permission

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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