Ideals in Parabolic Subalgebras of Simple Lie Algebras

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dc.creatorChari, Vyjayanthi
dc.creatorDolbin, R. J.
dc.creatorRidenour, T.
dc.date2008-09-01
dc.date.accessioned2026-07-07T09:59:45Z
dc.date.available2026-07-07T09:59:45Z
dc.descriptionWe study ad-nilpotent ideals of a parabolic subalgebra of a simple Lie algebra. Any such ideal determines an antichain in a set of positive roots of the simple Lie algebra. We give a necessary and sufficient condition for an antichain to determine an ad-nilpotent ideal of the parabolic. We write down all such antichains for the classical simple Lie algebras and in particular recover the results of D. Peterson. In section 2 of the paper we study the unique ideal in a parabolic which is irreducible as a module for the reductive part and give several equivalent statements that are satisfied by the corresponding subset of roots.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0809.0245
dc.identifierhttp://arxiv.org/abs/0809.0245
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168137
dc.subjectRepresentation Theory
dc.subject17B20
dc.titleIdeals in Parabolic Subalgebras of Simple Lie Algebras
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