Low Cohomogeneity and Polar Actions on Exceptional Compact Lie Groups

Details Low Cohomogeneity and Polar Actions on Exceptional Compact Lie Groups Low Cohomogeneity and Polar Actions on Exceptional Compact Lie Groups

2008-04-10

arxiv.org/abs/0804.1677v2

Transform. Groups 14 (2009), no. 2, 387--415

Mathematics

Differential Geometry

27 pages; introduction rewritten; references updated; final version; to appear in Transformation Groups

Scientific paper

10.1007/s00031-009-9052-2

We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. 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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