Microlocal KZ functors and rational Cherednik algebras

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 $\mathbb{Z}/l\mathbb{Z}$.

Revised to improve exposition, giving more details on the construction of the microlocal local systems and providing background information on twisted D-modules in an appendix

References in corpus (1)

• On the category O for rational Cherednik algebras

Cited by in corpus (1)

• Filtrations on Springer fiber cohomology and Kostka polynomials