Representation theory of the rational Cherednik algebras of type Z/lZ via microlocal analysis

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