Extensions of the Duflo map and Chern-Simons expectation values (Q2407365)

The Duflo map \(Q_D:\mathcal{S}(\mathfrak{g})\rightarrow \mathcal{U}(\mathfrak{g})\) is a map from the symmetric algebra \(\mathcal{S}(\mathfrak{g})\) over a Lie algebra \(\mathfrak{g}\) into its universal algebra \(\mathcal{U}(\mathfrak{g})\). More precisely, \(Q_D\) is a quantization map since it is a special case of Kontsevich's quantization of Poisson manifolds. By computing what the authors call \textit{the quantization of the exponential map} the result will be an operator-valued matrix that can be viewed as a quantum deformation of \(\mathrm{SU}(2)\). Also, the Duflo map is defined and evaluated on the particular type of non-gauge-invariant terms relevant for the current considerations. Finally, the Duflo map is used to quantize a specific function of flux operators.