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The bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equation correspondingto the affine Hecke algebra $H$ of type $A_{N-1}$ is a consistent system of$q$-difference equations which in some sense contains two families ofCherednik's quantum affine Knizhnik-Zamolodchikov equations for meromorphicfunctions with values in principal series representations of $H$. In this paperwe extend this construction of BqKZ to the case where $H$ is the affine Heckealgebra associated to an arbitrary irreducible reduced root system. Weconstruct explicit solutions of BqKZ and describe its correspondence to abispectral problem involving Macdonald's $q$-difference operators.

Bispectral quantum Knizhnik–Zamolodchikov equations for arbitrary root systems