A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras

In the representation theory of the group GLn(C), an important tool are the Young tableaux. The irreducible representations are in one-to-one correspondence with the shapes of these tableaux. Let T be the subgroup of diagonal matrices in GLn(C). Then there is a canonical way to assign a weight of T to any Young tableau such that the sum over the weights of all tableaux of a fixed shape is the character CharV of the corresponding GLn(C)-module V . Note that this gives not only a way to compute the character, it gives also a possibility to describe the multiplicity of a weight in the representation: It is the number of different tableaux of the same weight. Eventually, the Littlewood-Richardson rule describes the decomposition of tensor products of GLn(C)modules purely in terms of the combinatoric of these Young tableaux.