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Derived equivalences for Rational Cherednik algebras
Duke Mathematical Journal. 2017. Vol. 166. No. 1. P. 27-73.
Losev Ivan
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.
Publication based on the results of:
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For a complex reflection group W with reflection representation hh, we define and study a natural filtration by Serre subcategories of the category O_c(W,h) of representations of the rational Cherednik algebra H_c(W,h). This filtration refines the filtration by supports and is analogous to the Harish-Chandra series appearing in the representation theory of finite groups of ...
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Polishchuk A., Lekili Y., / Cornell University. Series arXiv "math". 2018.
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