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

Supported by the NSF under Grant DMS-1151473. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.