The Whitney presentation conjecture for quantum K-theory of partial flag varieties

Let $X=Fl(v_1,\dots,v_k;N)$ be the partial flag variety of flags $V_1\subset\dots\subset V_k\subset\mathbb{C}^N$ with $\dim(V_i)=v_i$. Let $\mathcal{S}_i$ be the tautological subbundles, with $\mathcal{S}_{i+1}=\mathbb{C}^N$, and let $\mathcal{R}_i=\mathcal{S}_{i+1}/\mathcal{S}_i$. Write $\Lambda_y(E)=\sum_j y^j[\wedge^jE]$, let $Q_i$ be the quantum parameter, and let $*$ denote quantum multiplication. The Whitney presentation conjecture. The relations in the $T$-equivariant quantum $K$-ring are

$$\Lambda_y(\mathcal{S}_i) * \Lambda_y( \mathcal{R}_i)=\Lambda_y( \mathcal{S}_{i+1})-y^{v_{i+1}-v_i}\frac{Q_i}{1-Q_i}\det(\mathcal{R}_i) *\left(\Lambda_y(\mathcal{S}_i)-\Lambda_y(\mathcal{S}_{i-1})\right).$$

This is a conjectural description motivated by the operator-product relations of a three-dimensional gauged linear sigma model; a proven description of the quantum $K$-ring of partial flag varieties was not known in the source context.