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The Partial Order of Dominant Weights

✍ Scribed by John R. Stembridge

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
511 KB
Volume
136
Category
Article
ISSN
0001-8708

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✦ Synopsis

The weight lattice of a crystallographic root system is partially ordered by the rule that *>+ if *&+ 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 * covers + in this partial order only if *&+ belongs to a distinguished subset of the positive roots. Also, if the root system is irreducible, we prove that the Mo bius function of the partial order takes on only the values [0, \1, \2].

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