Microlocalization of rational Cherednik algebras

Masaki Kashiwara, Raphael Rouquier

Published 2007-05-09, updated 2007-10-08Version 2

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.