Toward quantum Pieri rule for $F\ell_n$ via Seidel representation

Changzheng Li; Jiayu Song

Toward quantum Pieri rule for $F\ell_n$ via Seidel representation

Algebraic Geometry 2025-07-17 v1

Authors: Changzheng Li , Jiayu Song

Abstract

By using a ``quantum-to-classical" reduction formula on the Gromov-Witten invariants of flag vaireities $F\ell_n$ , we provide a new proof of the Seidel operator on the quantum cohomology ring $QH^*(F\ell_n)$ . Further, we reprove a quantum Pieri rule with respect to certain special Schubert class for $QH^*(F\ell_n)$ . Finally, we propose a concrete conjecture on the corresponding quantum Pieri rule for the quantum $K$ -theory of $F\ell_n$ .

Keywords

quantum cohomology Pieri rule flag variety Seidel representation Gromov-Witten invariant

Cite

@article{arxiv.2507.12351,
  title  = {Toward quantum Pieri rule for $F\ell_n$ via Seidel representation},
  author = {Changzheng Li and Jiayu Song},
  journal= {arXiv preprint arXiv:2507.12351},
  year   = {2025}
}

Comments

14 pages. This paper was written in Chinese, published at SCIENTIA SINICA Mathematica, 2024, 54(12): 2009-2022. This is an English translation for those who might be interested

Toward quantum Pieri rule for $F\ell_n$ via Seidel representation

Abstract

Keywords

Cite

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