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

Let W be the wreath product of a symmetric group with a cyclic group of order l. The corresponding restricted rational Cherednik algebra is a finite dimensional algebra whose block structure has a combinatorial description in terms of J-hearts. We show that this description is equivalent to one given in terms of residues of multipartitions. This establishes links with Rouquier families for the ...

We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group Sn over the complex numbers. Interestingly, the unitary representations in the category O for the rational Cherednik algebra of type A studied in [ESG] correspond to the unitary representations of the corresponding Hecke ...