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

Abstract

Based on the methods developed in [Kashiwara-Rouquier], we consider microlocalization of the rational Cherednik algebra of type $\mathbb{Z}/l\mathbb{Z}$. 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.

17 pages, AMSLaTeX with XYpic. Revised: the sign of parameters are modified