A conjecture on the Poincar{é}-Betti series of modules of differential operators on a generic hyperplane arrangement

Holm studied modules of higher order differential operators (generalising derivations) on generic (central) hyperplane arrangements. We use his results to determine the Hilbert series of these modules. We also give a conjecture about the Poincar{é}-Betti series; these are known for the module of derivations through the work of Yuzvinsky and of Rose and Terao.