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arxiv: 0705.1245 · v2 · submitted 2007-05-09 · 🧮 math.RT · math.AG· math.QA

Microlocalization of rational Cherednik algebras

classification 🧮 math.RT math.AGmath.QA
keywords microlocalizationalgebrascherednikmodulesrationalachievedcategorycertain
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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.

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