Open AccessFrom Jantzen to Andersen filtration via tilting equivalence
Author(s) -
Johannes Kübel
Publication year - 2012
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-15202
Subject(s) - mathematics , verma module , filtration (mathematics) , homomorphism , pure mathematics , equivalence (formal languages) , functor , covariance and contravariance of vectors , cartesian closed category , subcategory , isomorphism (crystallography) , crystallography , chemistry , lie algebra , crystal structure
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.