Unicity of graded covers of the Category $\mathcal O$ of   Bernstein-Gelfand-Gelfand
  We show that the standard graded cover of the well-known category $\mathcal O$ of Bernstein-Gelfand-Gelfand can be characterized by its compatibility with the action of the center of the enveloping algebra. 
Michael Rottmaier and Wolfgang Soergel
math.RT