Generalised Links–Gould polynomial conjecture for the Alexander polynomial

Let $L$ be an oriented link, let $m,n$ be positive integers, let $LG^{m,n}_L(\tau,t)$ denote the Links–Gould invariant, and let $\Delta_L$ denote the Alexander polynomial. Generalised Links–Gould conjecture.

$$LG^{m,n}_L(\tau,e^{\pi\sqrt{-1}/m})=\Delta_L(\tau^{2m})^n,$$

and, equivalently by the symmetry of $LG^{m,n}$,

$$LG^{m,n}_L(\tau,e^{\pi\sqrt{-1}/n})=\Delta_L(\tau^{2n})^m.$$

This conjecture proposes an extension of the established $n=1$ relation between the Links–Gould and Alexander polynomials. Its resolution is not indicated in the supplied text.