Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems

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The bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra H of type Aₙ₋₁ is a consistent system of q-difference equations which in some sense contains two families of Cherednik's quantum affine Knizhnik-Zamolodchikov equations for meromorphic functions with values in principal series representations of H. In this paper we extend this construction of BqKZ to the case where H is the affine Hecke algebra associated to an arbitrary irreducible reduced root system. We construct explicit solutions of BqKZ and describe its correspondence to a bispectral problem involving Macdonald's q-difference operators.