Twisted Hochschild Homology of Quantum Flag Manifolds and Kähler Forms

We study the twisted Hochschild homology of quantum flag manifolds, the twist being the modular automorphism of the Haar state. We prove that every quantum flag manifold admits a non-trivial class in degree two, with an explicit representative defined in terms of a certain projection. The corresponding classical two-form, via the Hochschild–Kostant–Rosenberg theorem, is identified with a Kähler form on the flag manifold.