Abstract:We study the $b$-$6j$ symbols -- an analytic extension of the $6j$-symbols for the principal series of the modular double of $\mathrm U_q\mathfrak{sl}(2;\mathbb R)$ -- with complex index $b,$ refereed to as the \emph{complex $b$-$6j$ symbols}. Then we relate their asymptotics, when the six parameters scale according to the dihedral angles of a hyperideal hyperbolic tetrahedron, to the volume and the determinant of the Gram matrix of the tetrahedron. In the case $\arg b=\pm \frac{\pi}{4},$ we believe that this work is closely related to the complex Liouville string\,\cite{CEMR}.
From: Tian Yang [view email]
[v1]
Tue, 2 Jun 2026 13:43:21 UTC (220 KB)
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