Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Details Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

2008-05-30

arxiv.org/abs/0805.4678v4

Symmetry, Integrability and Geometry: Methods and Applications 5, 044 (2009) http://www.emis.de/journals/SIGMA/2009/044/

Mathematics

Quantum Algebra

33 pages, 3 color figures

Scientific paper

10.3842/SIGMA.2009.044

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators, and, as a by-product, recover the known graphs E4(SU4), E6(SU4) and E8(SU4) describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoids.

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