Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds

We construct covariant q-deformed holomorphic structures for all finitely generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenberger–Kolb calculi. In classical limit, these reduce to of sections homogeneous vector bundles manifolds. For case simple modules, we show that this structure is unique. This generalises earlier work Majid, Khalkhali, Landi, and van Suijlekom line Podleś sphere, subsequent Khalkhali Moatadelro general projective space.