A combinatorial model for crystals of kac-moody algebras

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 λ-chain, which is a chain of positive roots defined by certain interlacing conditions.