Work

Quantum $K$-theoretic divisor axiom for flag manifolds

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.16150

Authors: Lenart, Cristian, Naito, Satoshi, Sagaki, Daisuke, Mihalcea, Leonardo C., Xu, Weihong

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415908214

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