  Cherednik's quantum affine Knizhnik-Zamolodchikov equations associated to an
affine Hecke algebra module M form a holonomic system of q-difference equations
acting on M-valued functions on a complex torus T. In this paper the quantum
affine Knizhnik-Zamolodchikov equations are related to the Cherednik-Macdonald
theory when M is induced from a character of a standard parabolic subalgebra of
the affine Hecke algebra. We set up correspondences between solutions of the
quantum affine KZ equations and, on the one hand, solutions to the spectral
problem of the Cherednik-Dunkl q-difference reflection operators (generalizing
work of Kasatani and Takeyama) and, on the other hand, solutions to the
spectral problem of the Cherednik-Macdonald q-difference operators
(generalizing work of Cherednik). The correspondences are applicable to all
relevant spaces of functions on T and for all parameter values, including the
cases that q and/or the Hecke algebra parameters are roots of unity.
