  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.
