Specializations of the Burau representation at roots of unity

The Burau representation and its specialisations at roots of unity are closely related to monodromy representations associated to families of cyclic coverings of a fixed degree of the projective line. If the number of ramifications is small relative to the degree, Deligne and Moscow constructed non arithmetic monodromy using these families. We show
that if the number of ramifications is sufficiently high relative to the degree, then the monodromy is an arithmetic group. The proof uses the existence of a large number of unipotent elements in the monodromy group in the relevant case.