An algebraic approach to the KZ-functor for rational Cherednik algebras associated with cyclic groups

We give a complete algebraic description of the KZ-functor for rational Cherednik algebras associated with cyclic groups for a subset of parameter values from which all parameter values can be obtained by integral translations. This is done by identifying the precise parameter values for which the projective object PKZPKZ is isomorphic to the Δ-module associated with the coinvariant algebra and by determining the action of the cyclotomic Hecke algebra on PKZPKZ in this case.