2010/02/18 by O. Barshevsky, Barshevsky, O., M. Fayers +3
Mathematics · #17B67 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B67
paper · pdf · doi:10.48550/arxiv.1002.3457
arxiv created 2011/12/07 · arxiv updated 2011/12/08
Let Λ be a dominant integral weight of level k for the affine Lie algebra \mathfrak 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.