Let \(\mathfrak{g}\) be a simple complex Lie algebra of a classical type and \({U}_{q}\left(\mathfrak{g}\right)\) the corresponding Drinfeld–Jimbo quantum group at q not a root of unity. With every point t of the fixed maximal torus T of an algebraic group G with Lie algebra \(\mathfrak{g}\) we associate an additive category \({\mathcal{O}}_{q}\left(t\right)\) of \({U}_{q}\left(\mathfrak{g}\right)\) -modules that is stable under tensor product with finite-dimensional quasiclassical \({U}_{q}\left(\mathfrak{g}\right)\) -modules. We prove that \({\mathcal{O}}_{q}\left(t\right)\) is essentially semi-simple and use it to explicitly quantize equivariant vector bundles on the conjugacy class of t.
