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Dirac cohomology and simple modules of the Dunkl-Opdam subalgebra via inherited Drinfeld properties

In this paper we define a new presentation for the Dunkl-Opdam subalgebra of the rational Cherednik algebra. This shows that the Dunkl-Opdam subalgebra is a Drinfeld algebra. We use this fact to define Dirac cohomology for the DO subalgebra. We also formalise generalised graded Hecke algebras and define a Langlands classification to generalised graded Hecke algebras.

preprint2018arXivOpen access
Kieran Calvert
math.RT
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Kieran Calvert

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