Microlocalization of rational Cherednik algebras

Details Microlocalization of rational Cherednik algebras Microlocalization of rational Cherednik algebras

2007-05-09

arxiv.org/abs/0705.1245v2

Mathematics

Representation Theory

36 pages, minor corrections, to appear in Duke Math. Journal

Scientific paper

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.

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