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.

47 pages, accepted by Represent. Theory

References in corpus (4)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Affine highest weight categories and affine quasihereditary algebras
• From double affine Hecke algebras to quantized affine Schur algebras

Cited by in corpus (1)

• Derived equivalences for trigonometric double affine Hecke algebras