%0 Journal Article
%T Hilbert schemes, wreath products, and the McKay correspondence
%A Weiqiang Wang
%J Mathematics
%D 1999
%I arXiv
%X Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1,Gr,S2,W], but direct connections are yet to be clarified to explain such a coincidence. We provide several non-trivial steps toward establishing our main conjecture on the isomorphism between the Hilbert quotient of the affine space $\C^{2n}$ by the wreath product $\G ~ S_n$ and Hilbert schemes of points on the minimal resolution of a simple singularity $\C^2 /\G$. We discuss further various implications of our main conjecture. We obtain a key ingredient toward a direct isomorphism between two forms of McKay correspondence in terms of Hilbert schemes [N1, Gr, N2] and respectively of wreath products [FJW]. We in addition establish a direct identification of various algebraic structures appearing in two different setups of equivariant K-theory [S2, W].
%U http://arxiv.org/abs/math/9912104v1