Abstract
Let $\mathscr {C}(S_n)$ be the $\mathbb {Z}$-module of integer-valued class functions on the symmetric group $S_n)$. We introduce a graded version of the convolution product on $\mathscr {C}(S_n)$, and we show that there is a degree-preserving ring isomorphism $\mathscr {C}(S_n)\longrightarrow H^\ast({\rm Hilb}^n(\mathbb {A_C}^2);\mathbb {Z})$ to the cohomology of the Hilbert scheme of points in the complex affine plane.
Citation
Manfred Lehn. Christoph Sorger. "Symmetric groups and the cup product on the cohomology of Hilbert schemes." Duke Math. J. 110 (2) 345 - 357, 1 November 2001. https://doi.org/10.1215/S0012-7094-01-11026-0
Information