The quantum K-theory realization conjecture for generalized flag varieties

Let $G$ be a simple Lie group with Borel subgroup $B$, let $G/B$ be its flag variety, let $P$ be the weight lattice, and let $R$ be the coefficient ring used in the quantum deformation. For each $\lambda\in P$, let $\widetilde{\Xi}^{[\lambda]}$ be the operator defined from a reduced alcove path, and let $R\langle\widetilde{[\alpha]},\alpha\in\Delta\rangle$ be the algebra generated by the deformed root operators. Denote the small quantum $K$-ring of $G/B$ by $QK(G/B)$. The quantum K-theory realization conjecture. The subalgebra generated by $\widetilde{\Xi}^{[\lambda]}$ for $\lambda\in P$ in $R\langle\widetilde{[\alpha]},\alpha\in\Delta\rangle$ is isomorphic to $QK(G/B)$. This proposes an algebraic realization of the small quantum $K$-ring of a generalized flag variety; the supplied text gives no evidence that the assertion has been proved or refuted.