8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation
Abstract
We study the vertex operators
Φ(z)
associated with standard quantum groups. The element
Z=R
R
t
is a "Casimir operator" for quantized Kac-Moody algebras and the quantum Knizhnik-Zamolodchikov (q-KZ) equation is interpreted as the statement
:ZΦ(z):=Φ(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.