From Jantzen to Andersen filtration via tilting equivalence

Johannes Kübel

Abstract


The space of homomorphisms between a projective object and a Verma module in category $\mathcal O$ inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Andersen filtration on the space of homomorphisms between a Verma module and a tilting module. Arkhipov's tilting functor, a contravariant self-equivalence of a certain subcategory of $\mathcal O$, which maps projective to tilting modules induces an isomorphism of these kinds of Hom-spaces. We show that this equivalence identifies both filtrations.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15202

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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