Koszul properties of the moment map of some classical representations

This work concerns the moment map μ associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that S/ (μ) , the coordinate algebra of the zero fibre of μ, be Koszul. The main result is that this algebra is not Koszul for the standard representation of sln, and of spn. This is deduced from a computation of the Betti numbers of S/ (μ) as an S-module, which are of interest also from the point of view of commutative algebra.