On flatness of Ocneanu's connections of the Dynkin diagrams and classification of subfactors
The author gives a proof of Ocneanu's announced classification of subfactors of the AFD type \(\text{II}_1\) factor with the principal graphs \(A_n\), \(D_n\), \(E_7\), the Dynkin diagrams, and gives a single explicit of \(\exp \pi\sqrt {-1}/ 24\) and \(\exp \pi\sqrt {-1}/ 60\) for each of \(E_6\) and \(E_8\) such that its validity is equivalent to the existence of two (and only two) subfactors for these principal graphs. His main tool is the flatness of connections on finite graphs, which is the key notion of Ocneanu's paragroup theory. He gives the difference between the diagrams \(D_{2n}\) and \(D_{2n+1}\) a meaning as a \(\mathbb{Z}/ 2\mathbb{Z}\)-obstruction for flatness arising in orbifold construction, which is an analogue of orbifold models in solvable lattice models.
flatness of connections on finite graphs
scientific article; zbMATH DE number 763981