Microlocalization of rational Cherednik algebras
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We construct a microlocalization of the rational Cherednik algebras $H$ of type $S_n$. This is achieved by a quantization of the Hilbert scheme $\Hilb^n\C^2$ of $n$ points in $\C^2$. We then prove the equivalence of the category of $H$-modules and the one of modules over its microlocalization under certain conditions on the parameter.
36 pages, minor corrections, to appear in Duke Math. Journal
36 pages, minor corrections, to appear in Duke Math. Journal