  We show that the spherical subalgebra of the rational Cherednik algebra
associated to the wreath product of a symmetric group and a cyclic group is
isomorphic to a quotient of the ring of invariant differential operators on a
space of representations of the cyclic quiver. This confirms a version of a
conjecture of Etingof and Ginzburg in the case of cyclic groups. The proof is a
straightforward application of work of Oblomkov on the deformed Harish-Chandra
homomorphism, and of Crawley-Boevey and of Gan and Ginzburg on preprojective
algebras.
