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Dualities and derived equivalences for category O
Univ Ghent, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.ORCID iD: 0000-0002-4633-6218
2017 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 219, no 2, 661-706 p.Article in journal (Refereed) Published
Abstract [en]

We determine the Ringel duals for all blocks in the parabolic versions of the BGG category associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary to the original category and the specific previously known cases in the parabolic setting, the blocks are not necessarily Ringel self-dual. However, the parabolic category as a whole is still Ringel self-dual. Furthermore, we use generalisations of the Ringel duality functor to obtain large classes of derived equivalences between blocks in parabolic and original category . We subsequently classify all derived equivalence classes of blocks of category in type A which preserve the Koszul grading.

Place, publisher, year, edition, pages
HEBREW UNIV MAGNES PRESS , 2017. Vol. 219, no 2, 661-706 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-324334DOI: 10.1007/s11856-017-1494-yISI: 000401257400007OAI: oai:DiVA.org:uu-324334DiVA: diva2:1110594
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2017-06-16 Created: 2017-06-16 Last updated: 2017-06-16Bibliographically approved

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Mazorchuk, Volodymyr
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