Properties of weight posets for weight multiplicity free representations

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dc.creatorPanyushev, Dmitri I.
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:39Z
dc.date.available2026-07-07T10:10:39Z
dc.descriptionWe 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 $0\le 2dim R-# E(R)$.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0810.2919
dc.identifierhttp://arxiv.org/abs/0810.2919
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171658
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleProperties of weight posets for weight multiplicity free representations
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