%0 Journal Article
%T Projective-injective modules, Serre functors and symmetric algebras
%A Volodymyr Mazorchuk
%A Catharina Stroppel
%J Mathematics
%D 2005
%I arXiv
%X We describe Serre functors for (generalisations of) the category O associated with a semi-simple complex Lie algebra. In our approach, projective-injective modules play an important role. They control the Serre functor in the case of a quasi-hereditary algebra having a double centraliser property with respect to a symmetric algebra. As an application of the double centraliser property and our description of Serre functors, we prove three conjectures of Khovanov about the projective-injective modules in the parabolic category O for sl_n.
%U http://arxiv.org/abs/math/0508119v2