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arXiv 2102.06672math.AGmath.AT
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旗型品种Chow环的余模结构计算

Computations of the Comodule Structures of the Chow rings of Flag Varieties

Rui Xiong

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摘要：

设$G$是一个连通的约化群，$G/B$是它的标志簇.设$π:G\to G/B$为自然投影。在本文中，我们开发了一个算法来描述的地图$π^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$的舒伯特细胞。利用Pieri规则，给出了上同调映射$π^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow \operatorname{CH}^*(G;\mathbb{F}_p)$的$A$ -型，$C$ -型，$G_2$，$F_4$的一个显式公式，并对$E_6$和$E_7$给出了$π^*$的一些部分结果.给出了上同调映射$μ:G\times G/B\to G/B$-型、$C$ -型、$G_2$、$F_4$的显式表示.

英文摘要：

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

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