On the Fusion Algebras of Bimodules Arising from Goodman-de la Harpe-Jones Subfactors

By using Ocneanu’s result on the classification of all irreducible connections on the Dynkin diagrams, we show that the dual principal graphs as well as the fusion rules of bimodules arising from any Goodman-de la Harpe-Jones subfactors are obtained by a purely combinatorial method. In particular we obtain the dual principal graph and the fusion rule of bimodules arising from the Goodmande la Harpe-Jones subfactor corresponding to the Dynkin diagram E8. As an application, we also show some subequivalence among A-D-E paragroups