Title: Computations of the Comodule Structures of the Chow rings of Flag Varieties Show Chinese title

Title: 旗流形的分次环余模结构的计算

Abstract: Let $G$ be a connected reductive group, and $G/B$ be its flag variety. Let $\pi:G\to G/B$ be the natural projection. In this paper, we developed an algorithm to describe the map $\pi^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$ in terms of Schubert cells. Taking advantage of the Pieri rule, we give an explicit formula for $A$-type, $C$-type, $G_2$, $F_4$ of the cohomology map $\pi^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$, and some partial result of $\pi^*$ is given for $E_6$ and $E_7$. Denote the group action map $\mu:G\times G/B\to G/B$, we also give an explicit formula for $A$-type, $C$-type, $G_2$, $F_4$ of the cohomology map $\mu^*: \operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G\times G/B;\mathbb{F}_p)$. Show Chinese abstract

Abstract: 设$G$为一个连通的半单群，$G/B$为其旗流形。 设$\pi:G\to G/B$为自然投影。 在本文中，我们开发了一个算法来用Schubert单元描述映射$\pi^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$。 利用Pieri法则，我们给出了上同调映射$\pi^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$的$A$型、$C$型、$G_2$、$F_4$的显式公式，并给出了$\pi^*$的一些部分结果对于$E_6$和$E_7$。 表示群作用映射$\mu:G\times G/B\to G/B$，我们还给出了上同调映射$\mu^*: \operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G\times G/B;\mathbb{F}_p)$的$A$类型，$C$类型，$G_2$，$F_4$的显式公式。