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- W145256870 abstract "We study weight posets of weight multiplicity free (=wmf) representations $R$ of reductive Lie algebras. Specifically, we are interested in relations between $dim R$ and the number of edges in the Hasse diagram of the corresponding weight poset, $# E(R)$. We compute the number of edges and upper covering polynomials for the weight posets of all wmf-representations. We also point out non-trivial isomorphisms between weight posets of different irreducible wmf-representations. Our main results concern wmf-representations associated with periodic gradings or Z-gradings of simple Lie algebras. For Z-gradings, we prove that $0< 2dim R-# E(R) < h$, where $h$ is the Coxeter number of $mathfrak g$. For periodic gradings, we prove that $0le 2dim R-# E(R)$." @default.
- W145256870 created "2016-06-24" @default.
- W145256870 creator A5059334014 @default.
- W145256870 date "2008-10-16" @default.
- W145256870 modified "2023-09-27" @default.
- W145256870 title "Properties of weight posets for weight multiplicity free representations" @default.
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- W145256870 hasPublicationYear "2008" @default.
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