A construction of generalized Harish-Chandra modules for locally reductive Lie algebras

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dc.creatorPenkov, Ivan
dc.creatorZuckerman, Gregg
dc.date2007-04-30
dc.date.accessioned2026-07-07T07:58:49Z
dc.date.available2026-07-07T07:58:49Z
dc.descriptionWe study cohomological induction for a pair $(\frak g,\frak k)$, $\frak g$ being an infinite dimensional locally reductive Lie algebra and $\frak k \subset\frak g$ being of the form $\frak k_0 + C_\gg(\frak k_0)$, where $\frak k_0\subset\frak g$ is a finite dimensional reductive in $\frak g$ subalgebra and $C_{\gg} (\frak k_0)$ is the centralizer of $\frak k_0$ in $\frak g$. We prove a general non-vanishing and $\frak k$-finiteness theorem for the output. This yields in particular simple $(\frak g,\frak k)$-modules of finite type over $\frak k$ which are analogs of the fundamental series of generalized Harish-Chandra modules constructed in \cite{PZ1} and \cite{PZ2}. We study explicit versions of the construction when $\frak g$ is a root-reductive or diagonal locally simple Lie algebra.
dc.identifierhttps://arxiv.org/abs/0704.3980
dc.identifierhttp://arxiv.org/abs/0704.3980
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128143
dc.subjectRepresentation Theory
dc.subject17B10; 17B55
dc.titleA construction of generalized Harish-Chandra modules for locally reductive Lie algebras
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