发表机构
Indian Institute of Technology Kanpur（坎普尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在带旗集值反向平面分割上构建Demazure晶体，统一推广了已知结构，并由此得到混合Grothendieck多项式的key多项式展开，进而将其表示为稳定与对偶稳定Grothendieck多项式的组合。
AI 中文摘要
本文在给定斜形状$\lambda/\mu$和旗$\Phi$的所有带旗集值反向平面分割的集合上构建了一个Demazure晶体结构。我们的构造统一推广了先前已知的关于所有带旗半标准集值表和所有带旗反向平面分割的Demazure晶体结构。因此，我们获得了由Guo--Kang--Liu引入的带旗混合Grothendieck多项式$H_{\lambda/\mu}(\mathbf{x}_{\Phi};\mathbf{t};\mathbf{w})$在key多项式方面的组合展开。应用此展开，我们将混合Grothendieck多项式$H_{\lambda/\mu}(\mathbf{x};\mathbf{t};\mathbf{w})$表示为稳定Grothendieck多项式$G_{\nu}(\mathbf{x})$和对偶稳定Grothendieck多项式$g_{\nu}(\mathbf{x})$的线性组合。
英文摘要
In this paper, we build a Demazure crystal structure on the set of all flagged set-valued reverse plane partitions of a given skew shape $λ/μ$ and flag $Φ$. Our construction provides a unified generalization of the Demazure crystal structures previously known for the set of all flagged semi-standard set-valued tableaux and the set of all flagged reverse plane partitions. Consequently, we obtain a combinatorial expansion for the flagged hybrid Grothendieck polynomial $H_{λ/μ}(\mathbf{x}_Φ;\mathbf{t};\mathbf{w})$, introduced by Guo--Kang--Liu, in terms of key polynomials. Applying this expansion, we express the hybrid Grothendieck polynomial $H_{λ/μ}(\mathbf{x};\mathbf{t};\mathbf{w})$ in terms of both the stable Grothendieck polynomials $G_ν(\mathbf{x})$ and the dual stable Grothendieck polynomials $g_ν(\mathbf{x})$.
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