Multiplicity Formulas for a Class of Representations of Affine Kac-Moody Algebras

Simple recursion formulas are derived for the multiplicities of the dominant weight vectors appearing in a class of irreducible highest weight representations of the indecomposable affine Kac-Moody algebras. This class is characterized by the appearance of exactly two distinct infinite sequences of dominant weight vectors. The general procedure used for the enumeration of these representations and for the derivation of the corresponding multiplicity formulas is that presented by Capps for the analysis of those irreducible representations containing exactly one such infinite sequence. This procedure includes the classification of representations in terms of congruence and the identification of Weyl orbits by the norm of the dominant weight. Some of the results presented have application to physical theories such as string field theories.