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arXiv · 2307.02782

Non-existence of exceptional orbits under polar actions on Hilbert spaces

Masahiro Morimoto
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Abstract

We prove that any polar action on a separable Hilbert space by a connected Hilbert Lie group does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmos in the finite dimensional Euclidean case. As an application, we give a simple geometric proof of the fact that any hyperpolar action on a simply connected compact Riemannian symmetric space by a connected Lie group does not have exceptional orbits.

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Masahiro Morimoto. 2023-07-06. Non-existence of exceptional orbits under polar actions on Hilbert spaces. https://arxiv.org/abs/2307.02782

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