Global quantum differential operators on quantum flag manifolds,
theorems of Duflo and Kostant

We give a short new proof for the theorem that global sections of the sheaf
of quantum differential operators on a quantum flag manifold are given by the
quantum group. As corollaries we retrieve Joseph and Letzter's quantum versions
of classical enveloping algebra theorems of Duflo and Kostant. We also describe
the center of the ad-integrable part of the quantum group and the adjoint Lie
algebra action on it.