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

Toshiro Kuwabara

Published 2010-03-17, updated 2010-07-11Version 2

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