Microlocal KZ functors and rational Cherednik algebras

TL;DR

This paper introduces a new family of exact functors from category O of rational Cherednik algebras to colored braid group representations, extending previous work and exploring more general complex reflection groups.

Contribution

It defines novel microlocal KZ functors for rational Cherednik algebras and generalizes their applicability beyond type A to complex reflection groups.

Findings

Calculated dimensions of representations from standard modules

Established functorial connections to colored braid groups

Extended constructions to complex reflection groups

Abstract

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