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 Uq(g)Uq(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.