author={John R. Stembridge},
  journal={Advances in Mathematics},
  • J. Stembridge
  • Published 25 June 1998
  • Mathematics
  • Advances in Mathematics
Abstract The weight lattice of a crystallographic root system is partially ordered by the rule that λ > μ if λ − μ is a nonnegative integer linear combination of positive roots. In this paper, we study the subposet formed by the dominant weights. In particular, we prove that λ covers μ in this partial order only if λ − μ belongs to a distinguished subset of the positive roots. Also, if the root system is irreducible, we prove that the Mobius function of the partial order takes on only the… 

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