Tensoring with infinite-dimensional modules in O_0
2010 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 13, no 5, 561-587 p.Article in journal (Refereed) Published
We show that the principal block O-0 of the BGG category O for a semi-simple Lie algebra g acts faithfully on itself via exact endofunctors which preserve tilting modules, via right exact endofunctors which preserve projective modules and via left exact endofunctors which preserve injective modules. The origin of all these functors is tensoring with arbitrary (not necessarily finite-dimensional) modules in the category O. We study such functors, describe their adjoints and show that they give rise to a natural (co) monad structure on O-0. Furthermore, all this generalises to parabolic subcategories of O-0. As an example, we present some explicit computations for the algebra sl(3).
Place, publisher, year, edition, pages
2010. Vol. 13, no 5, 561-587 p.
Tensor products, BGG category O
IdentifiersURN: urn:nbn:se:uu:diva-97776DOI: 10.1007/s10468-009-9137-6ISI: 000283587300004OAI: oai:DiVA.org:uu-97776DiVA: diva2:172843