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Kashiwara, Masaki; Rouquier, Raphaël

Microlocalization of rational Cherednik algebras. (English) Zbl 1147.14002

Duke Math. J. 144, No. 3, 525-573 (2008).
This paper gives a construction of a microlocalization of the rational Cherednik algebras of type \(S_n\). Let us first recall that such a rational Cherednik algebra is a one-parameter quantization of the algebra corresponding to the orbifold of \({\mathbb C}^{2 n}/S_n\). The microlocalization is obtained by a quantization of the Hilbert scheme of \(n\) points in \(\mathbb C^2\). The authors finally prove that there is an equivalence between the category of modules over rational Cherednik algebras and modules over the microlocalization.
Reviewer: Angela Gammella-Mathieu (Metz)

Cited in 1 Review
Cited in 19 Documents

MSC:

14A20 Generalizations (algebraic spaces, stacks)
14A22 Noncommutative algebraic geometry
16D90 Module categories in associative algebras
14C05 Parametrization (Chow and Hilbert schemes)
53D55 Deformation quantization, star products

Keywords:

rational Cherednik algebras; Hilbert scheme; microlocalization
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\textit{M. Kashiwara} and \textit{R. Rouquier}, Duke Math. J. 144, No. 3, 525--573 (2008; Zbl 1147.14002)
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