Quantum symmetries of graphs and higher Coxeter-Dynkin systems<

by Robert Coquereaux (Univ. Marseille)

Tuesday 1 Feb 2005, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

It has been known for a long time that conformal field theories defined on a torus -- affine WZW models of type SU(2) or minimal (Virasoro) models -- follow an ADE type classification (Dynkin diagrams). New diagrams were introduced in the 90's by P. Di Francesco and J.-B. Zuber in order to describe models of type SU(3). We describe quantum symmetries of graphs belonging to Dynkin diagrams or their higher analogues (higher Coxeter - Dynkin systems) by associating with every such diagram a quantum groupoid (a weak Hopf algebra) and two algebras of characters: one is related with the set of irreducible representations of quantum groups at roots of unity and the other with the Ocneanu graph of quantum symmetries. To every such quantum groupoid one can also associate several sets of generalized Racah-Wigner coefficients (Ocneanu cells and generalized 6J symbols). The aim of this seminar is to present a general introduction to the above ideas.