  We build representations of the elliptic braid group from the data of a
quantum D-module M over a ribbon Hopf algebra U. The construction is modelled
on, and generalizes, similar constructions by Lyubashenko and Majid, and also
certain geometric constructions of Calaque, Enriquez, and Etingof concerning
trigonometric Cherednik algebras. In this context, the former construction is
the special case where M is the basic representation, while the latter
construction can be recovered as a quasi-classical limit of U=U_t(sl_N), as t
limits 1. In the latter case, we produce representations of the double affine
Hecke algebra of type A_{n-1}, for each n.
