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

TL;DR

This paper establishes a cancellation-free version of the quantum K-theoretic divisor axiom specifically for flag manifolds in the quasi-minuscule case, refining previous results by removing cancellations.

Contribution

It provides a new formulation of the quantum K-theoretic divisor axiom that eliminates cancellations for quasi-minuscule fundamental weights in flag manifolds.

Findings

Removed cancellations from the quantum K-theoretic divisor axiom in the quasi-minuscule case.

Refined the understanding of quantum K-theoretic axioms for flag manifolds.

Extended previous work by Lenart-Naito-Sagaki-Xu with a cancellation-free formulation.

Abstract

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.