Representation Theory of Rational Cherednik Algebras of Type $\mathbb{Z}/l\mathbb{Z}$ via Microlocal Analysis

Abstract

Based on the methods developed in [KR], we consider microlocalization of rational Cherednik algebras of type $\mathbb{Z}/l\mathbb{Z}$. Our goal is to construct irreducible modules and standard modules of these rational Cherednik algebras by using microlocalization. As a consequence, we obtain sheaves corresponding to holonomic systems with regular singularities.