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Determination of quantum symmetries for higher ADE systems from the modular T matrix
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.Comment: 30 pages, 16 figures. Several misprints have been corrected. We added
several references and the appendix has been enlarged (one section on
essential paths and one section devoted to open problems). This article will
appear in the Journal of Mathematical Physic