Reduction algebra and differential operators on Lie groups

Let G be a connected and simply connected Lie group with Lie algebra g of finite dimension. Let h subset of g be a subalgebra, lambda a character of h, rho the trace of the adjoint representation and epsilon a formal parameter. We prove that the reduction algebra H-0(h(perpendicular to), lambda, q, epsilon) of Cattaneo-Felder for the Poisson manifold g* and the coisotropic submanifold -lambda + h(perpendicular to) is isomorphic with the algebra U(g, h, lambda + rho, epsilon)(h) of ad h-invariant differential operators on G/H. At the last section we prove further results relating various deformations and specializations at epsilon = 1 of these algebras.