Exceptional quantum groups

Abstract

The braids Rˇ, the underlying structure of the Boltzmann weight of a solvable lattice model, are obtained for the fundamental representation of the exceptional quantum group E 6. The symmetry properties of quantum Clebsch-Gordan coefficients and the braids Rˇ under Weyl-reflection are noted. The fusion matrices of the E 6 WZW models and the link polynomials are constructed. The symmetries of the braids Rˇ predict the symmetry of the Boltzmann weights of the vertex model based on E 6. The E 7 and F 4 quantum groups are briefly commented upon.