Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 1 (2017), 27-73.
Derived equivalences for rational Cherednik algebras
Let be a complex reflection group, and let be the rational Cherednik algebra for depending on a parameter . One can consider the category for . We prove a conjecture of Rouquier that the categories for and are derived-equivalent, provided that the parameters 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.
Duke Math. J., Volume 166, Number 1 (2017), 27-73.
Received: 23 September 2014
Revised: 16 September 2015
First available in Project Euclid: 1 September 2016
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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