Representation theory of the cyclotomic Cherednik algebra via the DunklOpdam subalgebra
Abstract
We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the OpdamDunkl 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 $\mathcal{O}$ to weighted KLR algebras, allows us to classify the simple DunklOpdam 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 3d gauge theories.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.05494
 Bibcode:
 2016arXiv160905494W
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory
 EPrint:
 30 pages. best viewed in PDF. v4: final version for publication