  We study the vertex operators $\Phi(z)$ associated with standard quantum
groups. The element $Z = RR^{t}$ is a "Casimir operator" for quantized
Kac-Moody algebras and the quantum Knizhnik-Zamolodchikov (q-KZ) equation is
interpreted as the statement $:Z\Phi(z): = \Phi(z)$. We study the covariance of
the q-KZ equation under twisting, first within the category of Hopf algebras,
and then in the wider context of quasi Hopf algebras. We obtain the
intertwining operators associated with the elliptic R-matrix and calculate the
two-point correlation function for the eight-vertex model.
