LIFTING CENTRAL INVARIANTS OF QUANTIZED HAMILTONIAN ACTIONS

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let * be a G-invariant Fedosov star-product on X such that the Hamiltonian action is quantized. We establish an isomorphism between the center of the quantum algebra K[X][[h]](G) and the algebra of formal power series with coefficients in the Poisson center of K[X](G).