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

الأصل · EN

Let Λ be a dominant integral weight of level k for the affine Lie algebra g and let α be a non-negative integral combination of simple roots. We address the question of whether the weight η=Λ-α lies in the set P(Λ) of weights in the irreducible highest-weight module with highest weight Λ. We give a non-recursive criterion in terms of the coefficients of α 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.