Differential forms via the Bernstein-Gelfand-Gelfand resolution for   quantized irreducible flag manifolds
  The quantum group version of the Bernstein-Gelfand-Gelfand resolution is used to construct a double complex of U_q(g)-modules with exact rows and columns. The locally finite dual of its total complex is identified with the de Rham complex for quantized irreducible flag manifolds. 
I. Heckenberger and S. Kolb