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

Abstract

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 (A3, A4). Some features relative to cells associated with more general ADE diagrams are also discussed.

arXiv comment52 pages, 27 figures. Version 2: Contents of subsections 2.6.3 and 3.8.1 have been changed. Fig. 9 was replaced. Updated and added references. Typos corrected

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• Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
• From modular invariants to graphs: the modular splitting method
• Topological defects in open string field theory
• Essential paths space on ADE SU(3) graphs: A geometric approach
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• About integer-valued variants of the theta and 6j symbols