Racah - Wigner quantum 6j Symbols, Ocneanu Cells for AN diagrams, and quantum groupoids

Robert Coquereaux (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We relate quantum 6J symbols of various types (quantum versions of Wigner and Racah symbols) to Ocneanu cells associated with AN Dynkin diagrams. We check explicitly the algebraic structure of the associated quantum groupoids and analyze several examples. Some features relative to cells associated with more general ADE diagrams are also discussed. Version 2: Subsection 2.6.3 was modified as well as two paragraphs in 3.8.1. Misprints corrected.

Mots clés: conformal field theories; Quantum 6J symbols; Wigner symbols; Racah symbols; Ocneanu cells; quantum groupoids; weak Hopf algebras; bigebras; fusion algebras; quantum symmetries; Coxeter-Dynkin diagrams; ADE; conformal field theories.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Algèbres quantiques [math.QA]

Robert Coquereaux. Racah - Wigner quantum 6j Symbols, Ocneanu Cells for AN diagrams, and quantum groupoids. Journal of Geometry and Physics, 2007, 57 (2). ⟨hal-00014523v2⟩