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Asymptotics of quantum $6j$ symbols

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arxiv 1706.04887 v3 pith:SQDXCIUI submitted 2017-06-15 math.QA math-phmath.GTmath.MP

classification math.QAmath-phmath.GTmath.MP
keywords asymptoticsquantumsymbolstermstetrahedronvolumecaseconjecture
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abstract

Asymptotics of quantum $6j$ symbols corresponding to a hyperbolic tetrahedra is investigated and the first two leading terms are determined for the case that the tetrahedron has a ideal or ultra-ideal vertex. These terms are given by the volume and the determinant of the Gram matrix of the tetrahedron. A relation to the volume conjecture of the Turaev-Viro invariant is also discussed.

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  1. On the asymptotic expansion of quantum invariants related to surgeries of Whitehead link I: Relative Reshetikhin-Turaev invariants and the Turaev-Viro invariants at $e^{\frac{2\pi\sqrt{-1}}{N+\frac{1}{2}}}$

    math.GT 2024-12 conditional novelty 5.0 of 10

    For rational surgeries on one component of the Whitehead link, the paper proves asymptotic expansions of the relative Reshetikhin-Turaev invariants and, under a large surgery coefficient condition, of the Turaev-Viro ...

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