Buch–Mihalcea's quantum K-theoretic divisor axiom for flag manifolds

Let $G$ be a connected, simply-connected, simple linear algebraic group over $\a0\mathbb{C}$ of Lie type $A$, let $P$ be a parabolic subgroup containing a maximal torus $T$ and a Borel subgroup $B$, and set $Y=G/P$. Let $d\in H_2(Y;\mathbb{Z})$ be an effective degree, let $\Omega_1,\Omega_2\subset Y$ be subvarieties in general position, and let ${\mathcal O}^{s_i}=[{\mathcal O}_{Y^{s_i}}]$ be the Schubert divisor class, with $d_i=\int_d[Y^{s_i}]$. Buch–Mihalcea's conjecture. For $m=3$,

$$\angles*{[{\mathcal O}_{\Omega_1}], [{\mathcal O}_{\Omega_2}], {\mathcal O}^{s_i}}^{Y}_{d} = \begin{cases} \angles*{[{\mathcal O}_{\Omega_1}], [{\mathcal O}_{\Omega_2}]}^{Y}_{d} & \text{if } d_i > 0, \\ \angles*{{\mathcal O}^{s_i}\cdot[{\mathcal O}_{\Omega_1}], [{\mathcal O}_{\Omega_2}]}_d^Y & \text{if } d_i=0, \end{cases}$$

where ${\mathcal O}^{s_i}\cdot[{\mathcal O}_{\Omega_1}]$ is the product in the ordinary $K$-theory ring $K(Y)$. This is a proposed $K$-theoretic analogue of the cohomological divisor axiom, which generally has no direct counterpart in $K$-theory; the statement concerns three-point quantum $K$-theoretic Gromov–Witten invariants and is asserted here for flag manifolds of Lie type $A$.