# THE PARTIAL ORDER OF DOMINANT WEIGHTS

@article{Stembridge1998THEPO, title={THE PARTIAL ORDER OF DOMINANT WEIGHTS}, author={John R. Stembridge}, journal={Advances in Mathematics}, year={1998}, volume={136}, pages={340-364} }

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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