On functors associated to a simple root

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dc.creatorMazorchuk, Volodymyr
dc.creatorStroppel, Catharina
dc.date2004-10-14
dc.date2007-04-05
dc.date.accessioned2026-07-07T07:54:53Z
dc.date.available2026-07-07T07:54:53Z
dc.descriptionAssociated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category $\mathcal{O}_0$. We study their relations, compute cohomologies of their derived functors and describe the monoid generated by Arkhipov's and Joseph's functors and the monoid generated by Irving's functors. It turns out that the endomorphism rings of all elements in these monoids are isomorphic. We prove that the functors give rise to an action of the singular braid monoid on the bounded derived category of $\mathcal{O}_0$. We also use Arkhipov's, Joseph's and Irving's functors to produce new generalized tilting modules.
dc.descriptionpresentation changed, pictures included
dc.identifierhttps://arxiv.org/abs/math/0410339
dc.identifierhttp://arxiv.org/abs/math/0410339
dc.identifierJournal of Algebra 2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126783
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject17B10, 20M05, 16G10
dc.titleOn functors associated to a simple root
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