Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): José Simental
We study Harish-Chandra bimodules over the rational Cherednik algebra $H_c(W)$ associated to a complex reflection group W with parameter c. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We classify those pairs of parameters $(c,c^{\prime })$ for which there exist fully supported Harish-Chandra bimodules, and give a description of the category of all Harish-Chandra bimodules modulo those without full support. When W is a symmetric group we are able to classify all irreducible Harish-Chandra bimodules. Our proofs are based on localization techniques, the action of the Namikawa–Weyl group on the set of parameters, and the study of partial KZ functors.