From Jantzen to Andersen filtration via tilting equivalence

• Autores: Johannes Kübel
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 2, 2012, págs. 161-180
• Idioma: inglés
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• Resumen

  • The space of homomorphisms between a projective object and a Verma module in category 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 O, which maps projective to tilting modules induces an isomorphism of these kinds of Hom-spaces. We show that this equivalence identifies both filtrations.