Extra structure on the cohomology of configuration spaces of closed orientable surfaces

The rational homology of unordered configuration spaces points on any surface was studied by Drummond-Cole and Knudsen. We compute the cohomology a closed orientable surface, keeping track mixed Hodge numbers action symplectic group cohomology. find series with coefficients in Grothendieck ring sp(2g) that describes explicitly decomposition into irreducible representations. From we deduce Betti numbers, obtaining new formula without cancellations.