Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a simple formula for this connected component, which applies to ‘most’ representations.

中文翻译：

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提升轨道空间的等距

给定一个紧群的正交表示，我们证明轨道空间等距群的连通分量的任何元素都提升到原始欧几里得空间的等变等距。推论包括这个连通分量的简单公式，它适用于“大多数”表示。