Microlocalization of rational Cherednik algebras

Abstract

We construct a microlocalization of the rational Cherednik algebras $H$ of type $S_n$. This is achieved by a quantization of the Hilbert scheme ${\mathrm{Hilb}}^n{\mathbb{C}}^2$ of $n$ points in ${\mathbb{C}}^2$. We then prove the equivalence of the category of $H$-modules and that of modules over its microlocalization under certain conditions on the parameter