Lattice of dominant weights of affine Kac–Moody algebras

Abstract

The dual space of the Cartan subalgebra in a Kac–Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac–Moody algebras. We give a more explicit description of the covering relations in this poset. We also study the structure of basic cells in this poset of dominant weights for untwisted affine Kac–Moody algebras of type A.