The flag-manifold Coulomb-branch relations conjecture

Let $Fl$ be the partial flag manifold with tautological bundles $\mathcal{S}_i$, let $X_a^{(i)}$ be variables interpreted as exponentials of the Chern roots of $\mathcal{S}_i$, and let $S_{k_i}$ act by permuting the variables $X_a^{(i)}$. Let $QK_T^\ell(Fl)$ denote the quantum $K$-ring twisted by

$$\prod_i\det^{-\ell_i}(\mathcal{S}_i).$$

Flag-manifold relations conjecture. For $\ell$ in the geometric window, the $\prod_i S_{k_i}$-invariant combinations of the Coulomb-branch equations generate the ideal of relations in $QK_T^\ell(Fl)$.

This is the flag-manifold analogue of the Grassmannian conjecture. The source establishes the correspondence between the symbols of difference operators and the Coulomb-branch equations, but the asserted generation of the twisted relation ideal remains open.