无穷小穿孔盘上主纤维丛的正则联络
Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc
摘要：
研究了无穷小穿孔圆盘上平凡代数G-主纤维丛的正则联络，其中G是特征为零的代数闭域上的连通约化线性代数群.证明了对于G的李代数中的某个X，每个正则联络到无穷小穿孔圆盘的适当覆盖的拉回规范等价于形式为X z^{-1}dz的联络.我们甚至可以安排ad X的唯一有理本征值为零。我们的结果允许分类的正规SL_n-连接规范等价。
英文摘要：
This paper concerns regular connections on trivial algebraic G-principal fiber bundles over the infinitesimal punctured disc, where G is a connected reductive linear algebraic group over an algebraically closed field of characteristic zero. We show that the pull-back of every regular connection to an appropriate covering of the infinitesimal punctured disc is gauge equivalent to a connection of the form X z^{-1}dz for some X in the Lie algebra of G. We may even arrange that the only rational eigenvalue of ad X is zero. Our results allow a classification of regular SL_n-connections up to gauge equivalence.
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