A Formula for K-Theory Truncation Schubert Calculus
A Formula for K-Theory Truncation Schubert Calculus
复制标题
K理论截断舒伯特微积分的公式
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Yong
中科院分区：
文献类型：
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作者：
A. Knutson;A. Yong
作者：Knutson， A；摘要：定义{x1，x2,x3，…}中多项式p的截断rt (p)作为除前T个变量外其他变量均为零的多项式。在某些好的情况下，舒伯特或格罗滕迪克多项式的截断可以再次成为舒伯特或格罗滕迪克多项式。我们利用这一现象给出了K （Flags (C^n)）中某些舒伯特结构常数的免减法公式，特别是推广了Kogan（2001）研究的仅处理上同调的公式，以及Buch（2002）研究的关于Grassmannian情况的公式。答案中的项是使用排列图上的“行进”操作计算的。
Author(s): Knutson, A; Yong, Alexander T | Abstract: Define a truncation rt (p) of a polynomial p in { x1,x2,x3,…} as the polynomial with all but the first t variables set to zero. In certain good cases, the truncation of a Schubert or Grothendieck polynomial may again be a Schubert or Grothendieck polynomial. We use this phenomenon to give subtraction-free formulas for certain Schubert structure constants in K ( Flags ( C^n)), in particular generalizing those studied by Kogan (2001) in which only cohomology was treated, and those studied by Buch (2002) on the Grassmannian case. The terms in the answer are computed using “marching” operations on permutation diagrams.