Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

Abstract

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the nilpotent representations (N-dimensional representations with q^2N=1) of U_q(sl(2)). We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the nilpotent representations by taking full advantage of the infinite dimensional colored representations of U_q(sl(2)). We construct invariants of trivalent colored oriented framed graphs from the nilpotent representations of U_q(sl(2)).