AI 中文总结
本文引入回稳定标准初等单项式及其完全齐次类似物，构成回稳定Schubert环的基，并用于表达移位特殊化多项式，恢复Stanley对称函数的系数。
AI 中文摘要
我们引入了回稳定标准初等单项式及其完全齐次类似物。这些族构成回稳定Schubert环的基，并记录了左稳定Schubert多项式的最终标准初等单项式展开。Dynkin反转交换这两个基，同时保持其系数不变。我们还证明了回稳定系数的轨道和恢复了Stanley对称函数的初等和完全齐次系数。最后，我们研究了由Fomin和Kirillov考虑的移位特殊化多项式$\mathcal{T}_w(t)=\mathfrak{S}_{1^t\times w}(1)$，它计算$1^t\times w$的约化管道梦想。我们用回稳定标准初等单项式系数表达了这个多项式。
英文摘要
We introduce back stable standard elementary monomials and their complete homogeneous analogues. These families form bases of the back stable Schubert ring and record the eventual standard elementary monomial expansions of left-stabilized Schubert polynomials. Dynkin reversal exchanges the two bases while preserving their coefficients. We also show that orbit sums of the back stable coefficients recover the elementary and complete homogeneous coefficients of Stanley symmetric functions. Finally, we study the shifted specialization polynomial $\mathcal{T}_w(t)=\mathfrak{S}_{1^t\times w}(1)$, considered by Fomin and Kirillov, which counts reduced pipe dreams of $1^t\times w$. We express this polynomial in terms of back stable standard elementary monomial coefficients.
Comments20 pages, 1 figure
