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

Abstract

In this article, we define an algebraic version of the Knizhnik--Zamolodchikov functor for the degenerate double affine Hecke algebras (a.k.a. trigonometric Cherednik algebras). We compare it with the KZ monodromy functor constructed by Varagnolo--Vasserot. We prove the double centraliser property for our functor and give a characterisation of its kernel. We establish these results for a family of algebras, called quiver double Hecke algebras, which includes the degenerate double affine Hecke algebras as special cases.

arXiv comment47 pages, accepted by Represent. Theory

References in corpus (11)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• On the category O for rational Cherednik algebras
• PBW bases and KLR algebras
• Affine highest weight categories and affine quasihereditary algebras
• Lecture notes on Cherednik algebras
• Homological properties of finite type Khovanov-Lauda-Rouquier algebras
• From double affine Hecke algebras to quantized affine Schur algebras
• Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra

Cited by in corpus (1)

• Derived equivalences for trigonometric double affine Hecke algebras