 

Ben Webster
Representation theory of the cyclotomic
Cherednik algebra via the DunklOpdam subalgebra
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Published: 
October 8, 2019. 
Keywords: 
Cherednik algebra, category O, Coulomb branch. 
Subject: 
16G99,17B37. 


Abstract
We give an alternate presentation of the cyclotomic rational Cherednik
algebra, which has the useful feature of compatibility with the
DunklOpdam 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
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. 

Acknowledgements
Supported by the NSF under Grant DMS1151473. 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.


Author information
Ben Webster:
Department of Pure Mathematics
University of Waterloo and Perimeter Institute for Mathematical Physics
Waterloo, ON, Canada
ben.webster@uwaterloo.ca

