Determination of quantum symmetries for higher ADE systems from the modular T matrix

Details Determination of quantum symmetries for higher ADE systems from the modular T matrix Determination of quantum symmetries for higher ADE systems from the modular T matrix

2002-03-26

arxiv.org/abs/hep-th/0203242v2

J.Math.Phys. 44 (2003) 3809-3837

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 16 figures. Several misprints have been corrected. We added several references and the appendix has been enlarged (o

Scientific paper

10.1063/1.1592609

We show that the Ocneanu algebra of quantum symmetries, for an ADE diagram (or for higher Coxeter-Dynkin systems, like the Di Francesco - Zuber system) is, in most cases, deduced from the structure of the modular T matrix in the A series. We recover in this way the (known) quantum symmetries of su(2) diagrams and illustrate our method by studying those associated with the three genuine exceptional diagrams of type su(3), namely E5, E9 and E21. This also provides the shortest way to the determination of twisted partition functions in boundary conformal field theory with defect lines.

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