On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume

Abstract

We generalize the colored Alexander invariant of knots to an invariant of graphs, and we construct a face model for this invariant by using the corresponding 6j-symbol, which comes from the non-integral representations of the quantum group U_q(sl_2). We call it the SL(2, C) quantum 6j-symbol, and show its relation to the hyperbolic volume of a truncated tetrahedron.

30 pages, typos, argument for the R-matrix is modified, Sections 2 and 3 are exchanged

References in corpus (6)

• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
• On the volume conjecture for hyperbolic knots
• Proof of the volume conjecture for Whitehead chains
• Polynomial 6j-Symbols and States Sums
• On invariants of graphs related to quantum $\mathfrak{sl}(2)$ at roots of unity

Cited by in corpus (5)

• Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
• Super-A-polynomial for knots and BPS states
• BTZ Black Hole Entropy and the Turaev-Viro model
• Polynomial 6j-Symbols and States Sums
• Braiding Operator via Quantum Cluster Algebra