Cancellation-free version of the quantum $K$-theoretic divisor axiom for the flag manifold in the quasi-minuscule case

We prove a cancellation-free version of the quantum $K$-theoretic divisor axiom for the flag manifold in the quasi-minuscule case. Namely, we remove the cancellations from the quantum $K$-theoretic divisor axiom due to Lenart-Naito-Sagaki-Xu in the case where the fundametal weight corresponding to the divisor class is quasi-minuscule.