There are two groups which act in a natural way on the bundle [Formula: see text] tangent to the total space [Formula: see text] of a principal [Formula: see text]-bundle [Formula: see text]: the group [Formula: see text] of automorphisms of [Formula: see text] covering the identity map of [Formula: see text] and the group [Formula: see text] tangent to the structural group [Formula: see text]. Let [Formula: see text] be the subgroup of those automorphisms which commute with the action of [Formula: see text]. In the paper, we investigate [Formula: see text]-invariant symplectic structures on the cotangent bundle [Formula: see text] which are in a one-to-one correspondence with elements of [Formula: see text]. Since, as it is shown here, the connections on [Formula: see text] are in a one-to-one correspondence with elements of the normal subgroup [Formula: see text] of [Formula: see text], so the symplectic structures related to them are also investigated. The Marsden–Weinstein reduction procedure for these symplectic structures is discussed.

中文翻译：

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主 G 束和相关辛结构上连接空间的对称性

有两个群以自然方式作用于束 [公式：参见文本] 与主体 [公式：参见文本]-束 [公式：参见文本] 的总空间 [公式：参见文本] 相切：该群[公式：见文]的[公式：见文]的自同构，涵盖[公式：见文]的恒等映射和与结构群[公式：见文]相切的群[公式：见文]。令 [Formula: see text] 是那些与 [Formula: see text] 的作用可对易的自同构的子群。在本文中，我们研究了余切丛 [Formula: see text] 上的 [Formula: see text]-不变辛结构，它们与 [Formula: see text] 的元素一一对应。因为，如此处所示，[公式：见文]与[公式：见文]的正规子群[公式：见文]的元素一一对应，因此也研究了与之相关的辛结构。讨论了这些辛结构的 Marsden-Weinstein 约简过程。