Weight modules of direct limit Lie algebras

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dc.creatorDimitrov, Ivan
dc.creatorPenkov, Ivan
dc.date1998-08-11
dc.date.accessioned2026-07-07T05:25:40Z
dc.date.available2026-07-07T05:25:40Z
dc.descriptionIn this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras $A(\infty)$, $B(\infty)$, $C(\infty)$ and $D(\infty)$. Our main tool is the shadow method introduced recently in \cite{DMP}. The integrable irreducible modules are an important particular class and we give an explicit parametrization of the finite integrable modules which are analogues of finite-dimensional irreducible modules over reductive Lie algebras. We then introduce the more general class of pseudo highest weight modules. Our most general result is the description of the support of any irreducible weight module.
dc.identifierhttps://arxiv.org/abs/math/9808045
dc.identifierhttp://arxiv.org/abs/math/9808045
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77268
dc.subjectRepresentation Theory
dc.subject17B10
dc.titleWeight modules of direct limit Lie algebras
dc.typetext

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