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.
Published
2012-06-01
How to Cite
Kübel, J. (2012). From Jantzen to Andersen filtration via tilting equivalence. MATHEMATICA SCANDINAVICA, 110(2), 161-180. https://doi.org/10.7146/math.scand.a-15202
Section
Articles