Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus

Abstract

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and co-semisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction - restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure).

25 pages, 5 tables, 9 figures. Version 2: updated references. Typos corrected. Several proofs added. Examples of ADE and generalized ADE trigonometric identities have been removed to shorten the paper

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• On some properties of SU(3) Fusion Coefficients
• Theta functions for lattices of SU(3) hyper-roots
• SU(3) higher roots and their lattices