Polar actions on symmetric spaces

Abstract

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry group and rank greater than one. In particular we show that these actions are hyperpolar, i.e. the sections are flat.

45 pages; erroneous Proposition 3.4 deleted; other minor changes and typos corrected; results remain unchanged

References in corpus (1)

• Coisotropic and polar actions on compact irreducible Hermitian symmetric spaces

Cited by in corpus (1)

• Twisted spin Sutherland models from quantum Hamiltonian reduction