Higher Coxeter graphs associated to affine su(3) modular invariants
Résumé
The affine su(3) modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs, called the Di Francesco-Zuber graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases, respectively associated to the subset of subgroup and module graphs. We provide a complete analysis of the subgroup graphs, which are those that admit a fusion graph algebra structure. We define their modular properties from induction-restriction maps and obtain the associated block-diagonal partition function. We show that the non block-diagonal partition functions are also obtained from these subgroup graphs, by the action of suitable modular invariant twists on their set of vertices.