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

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.

30 pages. best viewed in PDF. v4: final version for publication

References in corpus (2)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

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• Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras : algebraic theory