论文标题
硕士的H型结构常数的明确公式
Explicit Formulas for h-Deformed Structure Constants of Grassmannians
论文作者
论文摘要
格拉曼尼亚语中舒伯特细胞的Chern-Schwartz-Macpherson（CSM）和动机Chern（MC）类别是舒伯特品种在同胞和K理论中的基本类别的参数变形。像基本班级一样，变形班级构成了司硕的同事和K理论戒指的基础。本文的目的是根据多项式组合启动与基础CSM和MC类相关的结构常数的研究。首先，我们证明了涉及二项式系数的投影空间的结构常数。然后，使用残留微积分在Wieght函数上，我们描述了射影空间的结构常数和2平面草个性的某些相关结构常数为一个变量中显式多项式的系数。最后，我们提出了一种在这个方向上获得更一般结果的方法，并猜想概括了投影空间的上述结果。
The Chern-Schwartz-MacPherson (CSM) and motivic Chern (mC) classes of Schubert cells in a Grassmannian are one parameter deformations of the fundamental classes of the Schubert varieties in cohomology and K-theory respectively. Like the fundamental classes, the deformed classes form a basis for the cohomology and K-theory ring of the Grassmannian. The purpose of this paper is to initiate the study of the structure constants associated to the basis CSM and mC classes in terms of the combinatorics of polynomials. First, we prove formulas for the structure constants of projective spaces that involve binomial coefficients. Then, using residue calculus on wieght functions, we describe the structure constants of projective spaces and certain related structure constants of 2-plane Grassmannians as coefficients of explicit polynomials in one variable. Finally, we propose an approach for obtaining more general results in this direction, and make conjectures generalizing the aformentioned results for projective spaces.
