Representations of Cyclotomic Rational Cherednik Algebras with Aspherical Parameters

Abstract

In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_{\mathbf{c}}$ and its spherical subalgebra $e{H}_{\mathbf{c}}e$ with a Weil generic aspherical parameter $\mathbf{c}$, and further describe the simple modules in the category ${\mathcal{O}}_{\mathbf{c}}^{sph}$ . The main tools we use are categorical Kac-Moody actions on catogories ${\mathcal{O}}_{\mathbf{c}}$ and restriction functors for Harish-Chandra bimodules.

arXiv admin note: substantial text overlap with arXiv:1509.08550 by other authors