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arXiv · 1609.05494

Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra

Ben Webster
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Abstract

We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the Opdam-Dunkl 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 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.

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Ben Webster. 2016-09-18. Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra. https://arxiv.org/abs/1609.05494

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