## Duke Mathematical Journal

### Derived equivalences for rational Cherednik algebras

Ivan Losev

#### Abstract

Let $W$ be a complex reflection group, and let $H_{c}(W)$ be the rational Cherednik algebra for $W$ depending on a parameter $c$. One can consider the category $\mathcal{O}$ for $H_{c}(W)$. We prove a conjecture of Rouquier that the categories $\mathcal{O}$ for $H_{c}(W)$ and $H_{c'}(W)$ are derived-equivalent, provided that the parameters $c,c'$ have integral difference. Two main ingredients of the proof are a connection between the Ringel duality and Harish-Chandra bimodules and an analogue of a deformation technique developed by the author and Bezrukavnikov. We also show that some of the derived equivalences we construct are perverse.

#### Article information

Source
Duke Math. J., Volume 166, Number 1 (2017), 27-73.

Dates
Revised: 16 September 2015
First available in Project Euclid: 1 September 2016

https://projecteuclid.org/euclid.dmj/1472743767

Digital Object Identifier
doi:10.1215/00127094-3674223

Mathematical Reviews number (MathSciNet)
MR3592688

Zentralblatt MATH identifier
06686501

Subjects
Primary: 16E99: None of the above, but in this section
Secondary: 16G99: None of the above, but in this section

#### Citation

Losev, Ivan. Derived equivalences for rational Cherednik algebras. Duke Math. J. 166 (2017), no. 1, 27--73. doi:10.1215/00127094-3674223. https://projecteuclid.org/euclid.dmj/1472743767

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