We show that the quantum covering group associated to has an associated colored quantum knot invariant à la Reshetikhin–Turaev, which specializes to a quantum knot invariant for , and to the usual quantum knot invariant for . In particular, this furnishes an “odd” variant of quantum invariants, even for knots labeled by spin representations. We then show that these knot invariants are essentially the same, up to a change of variables and a constant factor depending on the knot and weight.
"Odd knot invariants from quantum covering groups." Algebr. Geom. Topol. 17 (5) 2961 - 3005, 2017. https://doi.org/10.2140/agt.2017.17.2961