The Lax-operator conjecture for Grassmannians

Let $G(r,s)$ be the Grassmannian and let $X_{[a,b]}$ be the variables indexed by $1\leq a\leq s-r$ and $1\leq b\leq r$, with $X_{a,b}=0$ when $a>s-r$ or $b>r$. Let $q$ be the quantum parameter, with $\log q\in H_2(G(r,s))$. Lax-operator conjecture. The Lax operator of $G(r,s)$ is

$$L(X)=X_{[1,1]}+\sum_{\begin{array}{c} {\scriptstyle 1\leq a\leq s-r} \\ {\scriptstyle 1\leq b\leq r} \end{array}}X_{[a,b]}^{-1}(X_{[a+1,b]}+X_{[a,b+1]})+qX_{[s-r,r]}^{-1}.$$

Such a formula would give an explicit Laurent-polynomial model for the Grassmannian Lax operator and is relevant to constructing mirrors of Calabi–Yau complete intersections in Grassmannians. The source attributes this conjecture to Eguchi, Hori, and Xiong and gives no resolution.