The Links–Quivers Correspondence for rational links

Let $L$ be a link with $|L|$ components, and let $P^{\bigwedge^j}_L(q,a)$ denote its $\bigwedge^j$-colored HOMFLY-PT polynomial. Define

$$P(L)=\sum_{j\geq 0}\left(\prod_{i=1}^j(1-q^{2i})\right)^{|L|-2}P^{\bigwedge^j}_L(q,a)x^j.$$

Let $P_Q(\overline{x})$ be the generating function associated with a symmetric quiver $Q$, evaluated at transformed variables $\overline{x}$. Links–Quivers Correspondence. For every link $L$, there is a symmetric quiver $Q_L$ such that $P(L)$ and $P_{Q_L}(\overline{x})$ are equal after a change of variables.

The correspondence relates generating functions of colored HOMFLY-PT polynomials to generating functions, and hence Donaldson–Thomas invariants, of symmetric quivers. The source presents this formulation as the standard Links–Quivers Correspondence and indicates that it will be given a new geometric interpretation for rational links; its resolution status is not specified here.