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Low cohomogeneity and polar actions on exceptional compact Lie groups

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We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a bi-invariant metric. We classify polar actions on these groups, in particular, we show that all polar actions are hyperpolar. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. Moreover, we determine the principal isotropy algebras for all isometric actions on G2.

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  1. Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Germany

    Andreas Kollross

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  1. Andreas Kollross
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Kollross, A. Low cohomogeneity and polar actions on exceptional compact Lie groups. Transformation Groups 14, 387–415 (2009). https://doi.org/10.1007/s00031-009-9052-2

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