On the colored Links--Gould polynomial

We give a cabling formula for the Links–Gould polynomial of knots colored with a $4n$-dimensional irreducible representation of ${\mathrm{U}}_q^H\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$ and identify them with the $V_n$-polynomial of knots for $n=2$. Using the cabling formula, we obtain genus bounds and a specialization to the Alexander polynomial for the colored Links–Gould polynomial that is independent of $n$, which implies corresponding properties of the $V_n$-polynomial for $n=2$ conjectured in previous work of two of the authors, and extends the work done for $n=1$. Combined with work of one of the authors arXiv:2409.03557, our genus bound for ${\mathrm{L}\mathrm{G}}^{(2)}=V_2$ is sharp for all knots with up to $16$ crossings.