AI 中文总结
针对$\tilde{A}_{n-1}$型仿射Kac–Moody群的旗簇，证明不同Weyl群对合对应的Schubert子簇在单位陪集点处的切锥不重合，推广了有限维情形的相关结果，所用技术工具涉及Weyl群嵌入组合学与幂么根基余伴随轨道。
AI 中文摘要
设G为$\tilde{A}_{n-1}$型仿射Kac–Moody群，B为G中的Iwahori子群，$\boldsymbol{\textit{F}}=G/B$为旗簇，W为G的Weyl群。对于W中不同的对合$w_1$、$w_2$，我们证明$\boldsymbol{\textit{F}}$的对应Schubert子簇$X_{w_1}$、$X_{w_2}$在点$p=e\bmod B$处的切锥$C_{w_1}$、$C_{w_2}$，作为$\boldsymbol{\textit{F}}$在点p处的切空间的子簇并不重合，这推广了有限维情形下的类似结果。所用主要技术工具是不同秩Weyl群嵌入的组合学，以及群B的幂么根基的余伴随轨道。
英文摘要
Let $G$ be the affine Kac--Moody group of type $\widetilde A_{n-1}$, $B$ be an Iwahori subgroup in $G$, $\mathcal{F}=G/B$ be the flag variety, and $W$ be the Weyl group of $G$. Given distinct involutions $w_1$, $w_2\in W$, we prove that the tangent cones $C_{w_1}$, $C_{w_2}$ to the corresponding Schubert subvarieties $X_{w_1}$ and $X_{w_2}$ of $\mathcal{F}$ at the point $p=e\mod B$ do not coincide as subvarieties of the tangent space to $\mathcal{F}$ at the point $p$. This generalizes similar results in the finite-dimensional setting. The main technical tools we used are combinatorics of the embeddings of the Weyl groups of different ranks and coadjoint orbits for the unipotent radical of the group $B$.
Comments15 pages
