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6j symbols for U_q(sl_2) and non-Euclidean tetrahedra

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arxiv math/0305113 v3 pith:UB6RC72D submitted 2003-05-07 math.QA math.SG

Yuka U. Taylor , Christopher T. Woodward This is my paper · ORCID
classification math.QAmath.SG
keywords formulasgeometrynon-euclideansymbolstetrahedraalgebraasymptoticsblocks
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We relate the semiclassical asymptotics of the 6j symbols for the representation theory of the quantized enveloping algebra U_q(sl_2) at q a primitive root of unity, or q positive real, to the geometry of non-Euclidean tetrahedra. The formulas are motivated by the geometry of conformal blocks in the Wess-Zumino-Witten model; they generalize formulas in the case q = 1 of Wigner, Ponzano and Regge, and Schulten and Gordon, proved by J. Roberts.

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Cited by 2 Pith papers

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  1. Quantum geometry from higher gauge theory

    gr-qc 2019-08 conditional novelty 7.0 of 10

    The BFCG-Yetter model and the KBF state sum produce the same single-4-simplex amplitude when evaluated on boundary states called G-networks.

  2. Les Houches lectures on Spinfoam Path Integrals

    gr-qc 2026-07 accept novelty 2.0 of 10

    A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.

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