Conformal embeddings and quantum graphs with self-fusion
Résumé
After a short description of the notion of quantum subgroups and quantum modules of quantum groups at roots of unity, in the framework of category theory, and a presentation of the known classifications (that we relate with the theory of conformal embeddings), we sketch several general methods of study and illustrate them on the particular example of a quantum subgroup of the non simple Lie group SU(2)xSU(3) stemming from a conformal embedding of the later, at level (16,6), into E_8. The graph describing its module structure over the corresponding fusion algebra incorporates several known components graphs of type SU(2) and SU(3), and it has self-fusion, but some of its components don't.
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