Microlocal KZ-functors and rational Cherednik algebras

Abstract

Following the work of Kashiwara and Rouquier and of Gan and Ginzburg, we define a family of exact functors from category $\mathcal{O}$ for the rational Cherednik algebra in type $A$ to representations of certain colored braid groups and we calculate the dimensions of the representations thus obtained from standard modules. To show that our constructions make sense in a more general context, we also briefly study the case of the rational Cherednik algebra corresponding to complex reflection group $\mathbb{Z}/l\mathbb{Z}$.