Combinatorial Models for Weyl Characters

Abstract

We present a set of axioms for combinatorial objects closely related to those for Kashiwara's crystals. We show that any model for the axioms, such as Littelmann's path model, has a character—a nonnegative sum of irreducible characters for a semisimple Lie group or algebra, or more generally, a symmetrizable Kac–Moody algebra. Moreover, there are simple explicit restriction rules and rules for decomposing the product of any such character by an irreducible character.