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<p>We provide a direct proof of the Seidel representation in the quantum <i>K</i>-theory <i>QK</i>(<i>Gr</i>(<i>k, n</i>)) by studying projected Gromov-Witten varieties concretely. As applications, we give an alternative proof of the <i>K</i>-theoretic quantum Pieri rule by Buch and Mihalcea (2011), reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for <i>K</i>(<i>Gr</i>(<i>k, n</i>)), and provide a quantum Littlewood-Richardson rule for <i>QK</i>(<i>Gr</i>(3, <i>n</i>)).</p>

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On Seidel representation in quantum K-theory of Grassmannians

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Changzheng Li,
  • Zhaoyang Liu,
  • Jiayu Song,
  • Mingzhi Yang

摘要

We provide a direct proof of the Seidel representation in the quantum K-theory QK(Gr(k, n)) by studying projected Gromov-Witten varieties concretely. As applications, we give an alternative proof of the K-theoretic quantum Pieri rule by Buch and Mihalcea (2011), reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k, n)), and provide a quantum Littlewood-Richardson rule for QK(Gr(3, n)).