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Regular version of the site

Article

Wreath Macdonald polynomials and categorical McKay correspondence

Cambridge Journal of Mathematics. 2014. Vol. 2. No. 2. P. 163-190.
Vologodsky V., Finkelberg M. V., Bezrukavnikov R.

Marc Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjecture where the symmetric group is replaced by the wreath product of S_n and Z/rZ. He has proven the original conjecture by establishing the geometric statement about the Hilbert scheme, as a byproduct he obtained a derived equivalence between coherent sheaves on the Hilbert scheme and coherent sheaves on the orbifold quotient of A^{2n} by the symmetric group S_n. A short proof of a similar derived equivalence for any symplectic quotient singularity has been obtained by the first author and Kaledin via quantization in positive characteristic. In the present note we prove various properties of these derived equivalences and then deduce generalized Macdonald positivity for wreath products.