Symmetric groups and the cup product on the cohomology of Hilbert schemes

Let C(S-n) be the Z-module of integer-valued class functions on the symmetr ic group Sn. We introduce a graded version of the convolution product on C( S-n), and we show that there is a degree-preserving ring isomorphism C(S-n) --> H*(Hilb(n)(A(C)(2));Z) to the cohomology of the Hilbert scheme of poin ts in the complex affine plane.