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arXiv · 2505.16150

Quantum $K$-theoretic divisor axiom for flag manifolds

Cristian Lenart·Satoshi Naito·Daisuke Sagaki·Leonardo C. Mihalcea·Weihong Xu
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Abstract

We prove an identity for (torus-equivariant) 3-point, genus 0, $K$-theoretic Gromov-Witten invariants of flag manifolds $G/P$, which can be thought of as a replacement for the ``divisor axiom'' in their (torus-equivariant) quantum $K$-theory. This identity enables us to compute these invariants when two insertions are Schubert classes and the other a Schubert divisor class. Our type-independent proof utilizes the Chevalley formula for the (torus-equivariant) quantum $K$-theory ring of flag manifolds, which computes multiplications by Schubert divisor classes in terms of the quantum Bruhat graph.

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Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Leonardo C. Mihalcea, Weihong Xu. 2025-10-31. Quantum $K$-theoretic divisor axiom for flag manifolds. https://arxiv.org/abs/2505.16150

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