Representation theory of the cyclotomicCherednik algebra via the Dunkl-Opdam subalgebra

摘要

We give an alternate presentation of the cyclotomic rational Cherednikalgebra, which has the useful feature of compatibility with theDunkl-Opdam subalgebra. This presentation has a diagrammatic flavor,and it provides a simple explanation of several surprising facts aboutthis algebra. It allows direct proof of the connection of categoryO to weighted KLR algebras, allows us to classify the simpleDunkl-Opdam modules over the Cherednik algebra and provides analgebraic construction of the KZ functor. Furthermore, one of primemotivations for considering this approach is to provide a better framework for connecting Cherednikalgebras to Coulomb branches of 3-d gauge theories.