A Combinatorial Model for Crystals of Kac-Moody Algebras

Details A Combinatorial Model for Crystals of Kac-Moody Algebras A Combinatorial Model for Crystals of Kac-Moody Algebras

2005-02-07

arxiv.org/abs/math/0502147v4

Mathematics

Representation Theory

28 pages, 2 figures

Scientific paper

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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