Extensions of the Duflo map and Chern-Simons expectation values

The Duflo map is a valuable tool for operator ordering in contexts in which the Kirillov-Kostant-Souriau bracket and its quantization play a role. It has beautiful properties on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. In the present work, we focus on its action beyond this subspace: We calculate the image of the exponential map, to obtain a certain deformation of SU(2), and we discuss and compare modifications of its action on non-invariant elements. Also, an application to the calculation of Chern-Simons theory expectation values is discussed.