Derived equivalences for Rational Cherednik algebras
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.
Cite
@article{arxiv.1406.7502,
title = {Derived equivalences for Rational Cherednik algebras},
author = {Ivan Losev},
journal= {arXiv preprint arXiv:1406.7502},
year = {2017}
}
Comments
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