A Lattice Model of Local Algebras of Observables and Elds with Braid Group Statistics

Using the 6j-symbols and the R-matrix for the quantum group S l q (2; C) at roots of unity we construct local algebras of observables and elds with braid group statistics on the lattice Z. These algebras are closely related to the XXZ-Heisenberg model and the RSOS models thus exhibiting the quantum group symmetry of these models. Our discussion relates the theory of integrable lattice models to the Doplicher-Haag-Roberts theory of superselection sectors. The construction of these algebras is a variant of the path space construction of Ocneanu and Sunder which replaces the usual tensor product construction of lattice models in statistical mechanics and extends previous discussions by Pasquier. Our construction is based on the theory of coloured graphs on S 2 and the associated Wigner-Eckhart theorem obtained previously by the authors.