  We report on a new approach to the calculation of Chern-Simons theory
expectation values, using the mathematical underpinnings of loop quantum
gravity, as well as the Duflo map, a quantization map for functions on Lie
algebras. These new developments can be used in the quantum theory for certain
types of black hole horizons, and they may offer new insights for loop quantum
gravity, Chern-Simons theory and the theory of quantum groups.
