De Rham complex for quantized irreducible flag manifolds

It is shown that quantized irreducible flag manifolds possess a canonical q-analogue of the de Rham complex. Generalizing the well-known situation for the standard Podleśʹ quantum sphere this analogue is obtained as the universal differential calculus of a distinguished first order differential calculus. The corresponding differential d can be written as a sum of differentials ∂ and . The universal differential calculus corresponding to the first order differential calculi d, ∂, and are given in terms of generators and relations. Relations to well-known quantized exterior algebras are established. The dimensions of the homogeneous components are shown to be the same as in the classical case. The existence of a volume form is proven.