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

Abstract In this paper, we define a new presentation for the Dunkl-Opdam subalgebra of the rational Cherednik algebra. This presentation uncovers the Dunkl-Opdam subalgebra as a Drinfeld algebra. We use… Click to show full abstract

Abstract In this paper, we define a new presentation for the Dunkl-Opdam subalgebra of the rational Cherednik algebra. This presentation uncovers the Dunkl-Opdam subalgebra as a Drinfeld algebra. We use this fact to define Dirac cohomology for the DO subalgebra. We also formalize generalized graded Hecke algebras and extend a Langlands classification to generalized graded Hecke algebras.

Keywords: dunkl opdam; drinfeld; dirac cohomology; opdam subalgebra

Journal Title: Communications in Algebra
Year Published: 2018

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