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arXiv · 1406.7502

Derived equivalences for Rational Cherednik algebras

Ivan Losev
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Abstract

Let W be a complex reflection group and H_c(W) the Rational Cherednik algebra for $W$ depending on a parameter c. One can consider the category O for H_c(W). We prove a conjecture of Rouquier that the categories O for H_c(W) and H_{c'}(W) are derived equivalent provided 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 analog of a deformation technique developed by the author and Bezrukavnikov. We also show that some of the derived equivalences we construct are perverse.

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BibTeXRIS

Ivan Losev. 2014-06-29. Derived equivalences for Rational Cherednik algebras. https://doi.org/10.1215/00127094-3674223

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