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

Abstract

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.

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 Physics

References in corpus (5)

• Generalised twisted partition functions
• The many faces of Ocneanu cells
• Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries
• Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
• On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories

Cited by in corpus (6)

• Comments about quantum symmetries of SU(3) graphs
• From conformal embeddings to quantum symmetries: an exceptional SU(4) example
• Racah - Wigner quantum 6j Symbols, Ocneanu Cells for AN diagrams, and quantum groupoids
• Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
• Torus structure on graphs and twisted partition functions for minimal and affine models
• From modular invariants to graphs: the modular splitting method