Abstract Grothendieck polynomials, introduced by Lascoux and Schutzenberger, are certain K-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the K-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and study their stable limits. We show that each of the K-theoretic Schur P-functions of Ikeda and Naruse arises from a limiting procedure applied to symplectic Grothendieck polynomials representing certain “Grassmannian” orbit closures.

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关于辛格洛腾迪克多项式的一些性质

摘要 格罗腾迪克多项式由 Lascoux 和 Schutzenberger 引入，是 Schubert 变体的某些 K 理论代表。辛格洛腾迪克多项式，最近由 Wyser 和 Yong 描述，代表了作用于完整标志变体的复辛群的轨道闭合的 K 理论类。我们证明了辛格洛腾迪克多项式的转换公式并研究了它们的稳定极限。我们证明了 Ikeda 和 Naruse 的每个 K 理论 Schur P 函数都来自应用于代表某些“格拉斯曼”轨道闭合的辛格罗腾迪克多项式的限制程序。