EXCEPTIONAL QUANTUM GROUPS

The braids R ̌, the underlying structure of the Boltzmann weight of a solvable lattice model, are obtained for the fundamental representation of the exceptional quantum group E6. The symmetry properties of quantum Clebsch-Gordan coefficients and the braids R ̌ under Weyl-reflection are noted. The fusion matrices of the E6 WZW models and the link polynomials are constructed. The symmetries of the braids R ̌ predict the symmetry of the Boltzmann weights of the vertex model based on E6. The E7 and F4 quantum groups are briefly commented upon. © 1990.