Yokota type invariants derived from non-integral highest weight representations of \(\mathcal U_q(sl_2)\) (Q2827536)

In this paper the authors use non-integral highest weight representations of the quantum enveloping algebra \(U_q(sl_2)\) to define invariants for colored oriented spatial graphs, whose valencies are greater than or equal to three. The authors propose a version of the volume conjecture for these invariants in the case of planar graphs. The conjecture relates the invariants to the volume of certain hyperbolic convex polyhedra corresponding to the graphs. The conjecture is checked numerically for some hyperbolic square pyramids and pentagonal pyramids.