  Cherednik attached to an affine Hecke algebra module a compatible system of
difference equations, called quantum affine Knizhnik-Zamolodchikov (KZ)
equations. In case of a principal series module we construct a basis of power
series solutions of the quantum affine KZ equations. Relating the bases for
different asymptotic sectors gives rise to a Weyl group cocycle, which we
compute explicitly in terms of theta functions. For the spin representation of
the affine Hecke algebra of type C the quantum affine KZ equations become the
boundary qKZ equations associated to the Heisenberg spin-1/2 XXZ chain. We show
that in this special case the results lead to an explicit 4-parameter family of
elliptic solutions of the dynamical reflection equation associated to Baxter's
8-vertex face dynamical R-matrix. We use these solutions to define an explicit
9-parameter elliptic family of boundary quantum Knizhnik-Zamolodchikov-Bernard
(KZB) equations.
