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15 January 2017 Derived equivalences for rational Cherednik algebras
Ivan Losev
Duke Math. J. 166(1): 27-73 (15 January 2017). DOI: 10.1215/00127094-3674223

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.

Citation

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Ivan Losev. "Derived equivalences for rational Cherednik algebras." Duke Math. J. 166 (1) 27 - 73, 15 January 2017. https://doi.org/10.1215/00127094-3674223

Information

Received: 23 September 2014; Revised: 16 September 2015; Published: 15 January 2017
First available in Project Euclid: 1 September 2016

zbMATH: 06686501
MathSciNet: MR3592688
Digital Object Identifier: 10.1215/00127094-3674223

Subjects:
Primary: 16E99
Secondary: 16G99

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 1 • 15 January 2017
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