Lifting isometries of orbit spaces
Metric Geometry
2021-09-17 v2 Differential Geometry
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2004.00097,
title = {Lifting isometries of orbit spaces},
author = {Ricardo A. E. Mendes},
journal= {arXiv preprint arXiv:2004.00097},
year = {2021}
}
Comments
9 pages. Final version, to appear in the Bulletin of the London Mathematical Society. Compared to the previous version, one of the corollaries to the main result has been reformulated as an easy-to-use formula (Proposition 5(b)). Moreover, many improvements to the presentation have been made, including the addition of a new section (Section 2)