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In the case of rational Cherednik algebras associated with cyclic groups, wegive an alternative proof that the projective object $P_{\text{KZ}}$representing the KZ-functor is isomorphic to the $\Delta$-module associatedwith the coinvariant algebra for a subset of parameter values from which allparameter values can be obtained by integral translations. We also specify theexact parameter values for which this isomorphism occurs. Furthermore, wedetermine the action of the cyclotomic Hecke algebra on $P_{\text{KZ}}$ forthese parameter values, thereby giving a complete algebraic description of theKZ-functor in this case.

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