发表机构
Shiv Nadar University; Kerala School of Mathematics（锡瓦纳德大学; 喀拉拉数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对曲线上带抛物结构的主丛，给出其结构群约化上存在抛物李代数丛联络的判据，并证明主丛的Harder-Narasimhan约化满足该条件。
AI 中文摘要
设X为紧致连通黎曼曲面，S⊂X为有限子集，考虑X上带S处抛物结构的抛物主G-丛ℰ_G，其中G为连通复约化仿射代数群。设P⊂G为抛物子群，ℰ_P⊂ℰ_G为ℰ_G到P的结构群约化。对(X,S)上任意锚映射非满射的抛物李代数丛，本文给出ℰ_P上存在抛物李代数丛联络的判据：当结构群约化ℰ_P⊂ℰ_G是抛物无穷小刚性时，ℰ_P容许抛物李代数丛联络。特别地，ℰ_G的Harder-Narasimhan约化容许抛物李代数丛联络。
英文摘要
Let $X$ be a compact connected Riemann surface and $S\,\subset\, X$ a finite subset. We consider parabolic principal $G$--bundles $\mathcal{E}_{G}$ on $X$ with parabolic structure on $S$, where $G$ is a connected complex reductive affine algebraic group. Let $P\, \subset\, G$ be a parabolic subgroup and $\mathcal{E}_{P}\, \subset\, \mathcal{E}_{G}$ a reduction of structure group of $\mathcal{E}_{G}$ to $P$. We give a criterion for the existence of a parabolic Lie algebroid connection on $\mathcal{E}_{P}$ for any given parabolic Lie algebroid on $(X,\,S)$ whose anchor map is not surjective. More precisely, $\mathcal{E}_{P}$ admits a parabolic Lie algebroid connection if the reduction $\mathcal{E}_{P}\, \subset\, \mathcal{E}_{G}$ is parabolically infinitesimally rigid. In particular, the Harder--Narasimhan reduction of $\mathcal{E}_{G}$ admits a parabolic Lie algebroid connection.
Comments20 Pages. To appear in Mediterranean Journal of Mathematics
