The Grassmannian Coulomb-branch relations conjecture

Let $\operatorname{Gr}(k,n)$ be the Grassmannian, let $\mathcal{S}$ be its tautological bundle, and let $X_a$ be variables interpreted as the exponentials of the Chern roots of $\mathcal{S}$. Let $QK_T^\ell(\operatorname{Gr}(k,n))$ be twisted quantum $K$-theory, with twisting determined by $\det^{-\ell}(\mathcal{S})$. Assume

$$-k<\ell\leq n-k+1.$$

Grassmannian relations conjecture. Symmetric combinations of the equations

$$(-1)^{k-1}X_a^\ell q\prod_b\frac{X_a}{X_b}=\prod_i\left(1-\frac{X_a}{\Lambda_i}\right)$$

generate the ideal of relations in $QK_T^\ell(\operatorname{Gr}(k,n))$.

This extends the analogous result in ordinary quantum $K$-theory to the specified range of twisted levels. The source derives the equations from difference operators, but the asserted generation of the twisted ring's relation ideal remains conjectural.