8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation

Details 8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation 8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation

1997-09-18

arxiv.org/abs/q-alg/9709028v1

Rev. Math. Phys. 10 (1998) 1027-1059

Mathematics

Quantum Algebra

31 pages. Plain TeX

Scientific paper

10.1142/S0129055X98000331

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.

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