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 $eH_\mathbf{c} e$ with a Weil generic aspherical parameter $\mathbf{c}$, and further describe the simple modules in the category $\mathcal{O}^{sph}_\mathbf{c}$. The main tools we use are categorical Kac-Moody actions on catogories $\mathcal{O}_\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.