Applications of the category of linear complexes of tilting modules   associated with the category O
  We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category O. 
Volodymyr Mazorchuk