Derived equivalences for Rational Cherednik algebras
arXiv:1406.7502 · doi:10.1215/00127094-3674223
Abstract
Let W be a complex reflection group and H_c(W) the Rational Cherednik algebra for 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.
32 pages, preliminary version; v2 33 pages some proofs rewritten; v3 32 pages, proofs of the main results substantially simplified, other minor changes; v4 some proofs were modified, other minor changes