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

TL;DR

This paper explores the relationship between quantum 6J symbols, Ocneanu cells, and quantum groupoids, providing explicit algebraic structures and examples for A3 and A4 diagrams, with discussions on ADE diagrams.

Contribution

It establishes a connection between quantum 6J symbols and Ocneanu cells, and analyzes the algebraic structure of related quantum groupoids with concrete examples.

Findings

Explicit algebraic structures for quantum groupoids associated with A3 and A4 diagrams

Demonstrated correspondence between quantum 6J symbols and Ocneanu cells

Discussion on features of cells related to ADE diagrams

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.