Duke Mathematical Journal

Derived equivalences for rational Cherednik algebras

Ivan Losev

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Abstract

Let W be a complex reflection group, and let Hc(W) be the rational Cherednik algebra for W depending on a parameter c. One can consider the category O for Hc(W). We prove a conjecture of Rouquier that the categories O for Hc(W) and Hc'(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
Received: 23 September 2014
Revised: 16 September 2015
First available in Project Euclid: 1 September 2016

Permanent link to this document
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

Keywords
rational Cherednik algebra category $\mathcal{O}$ derived equivalence Harish-Chandra bimodule perverse equivalence

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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