Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariants

Abstract

We show that the quantum covering group associated to osp(1|2n) has an associated colored quantum knot invariant \`a la Reshetikhin-Turaev, which specializes to a quantum knot invariant for osp(1|2n), and to the usual quantum knot invariant for so(1+2n). We then show that these knot invariants are the same, up to a change of variables and a constant factor depending on the knot and weight.