Quantum $K$-theoretic divisor axiom for flag manifolds
Quantum Algebra
2025-11-03 v2 Algebraic Geometry
Combinatorics
K-Theory and Homology
Representation Theory
Abstract
We prove an identity for (torus-equivariant) 3-point, genus 0, -theoretic Gromov-Witten invariants of flag manifolds , which can be thought of as a replacement for the ``divisor axiom'' in their (torus-equivariant) quantum -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 -theory ring of flag manifolds, which computes multiplications by Schubert divisor classes in terms of the quantum Bruhat graph.
Cite
@article{arxiv.2505.16150,
title = {Quantum $K$-theoretic divisor axiom for flag manifolds},
author = {Cristian Lenart and Satoshi Naito and Daisuke Sagaki and Leonardo C. Mihalcea and Weihong Xu},
journal= {arXiv preprint arXiv:2505.16150},
year = {2025}
}
Comments
All but Appendix A are written by Cristian Lenart, Satoshi Naito, Daisuke Sagaki, and Weihong Xu; Appendix A is written by Leonardo C. Mihalcea and Weihong Xu