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

TL;DR

This paper demonstrates that quantum knot invariants derived from osp(1|2n) and so(2n+1) quantum groups are essentially equivalent, differing only by a change of variables and a constant factor.

Contribution

It establishes the equivalence of quantum knot invariants from osp(1|2n) and so(2n+1) quantum groups, revealing a deep connection between these invariants.

Findings

Quantum osp(1|2n) knot invariants are equivalent to quantum so(2n+1) knot invariants.

The invariants differ only by a change of variables and a constant factor.

The result unifies two classes of quantum 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.