A non-recursive criterion for weights of a highest weight module for an affine Lie algebra

Abstract

Let $\Lambda$ be a dominant integral weight of level $k$ for the affine Lie algebra $\mathfrak{g}$ and let $\alpha$ be a non-negative integral combination of simple roots. We address the question of whether the weight $\eta =\Lambda -\alpha$ lies in the set $P(\Lambda )$ of weights in the irreducible highest-weight module with highest weight $\Lambda$. We give a non-recursive criterion in terms of the coefficients of $\alpha$ modulo an integral lattice $kM$, where $M$ is the lattice parameterizing the abelian normal subgroup $T$ of the Weyl group. The criterion requires the preliminary computation of a set no larger than the fundamental region for $kM$, and we show how this set can be efficiently calculated.

References in corpus (1)

• Blocks of cyclotomic Hecke algebras

Cited by in corpus (1)

• On multiplicities of maximal weights of $\widehat{sl}(n)$-modules