Orbits of the isotropy group action on quaternionic symmetric spaces (Q6621554)

The author studies the orbits of the isotropy subgroup of (the identity component of) the isometry group of a Wolf space, i.e., a quaternionic Kähler symmetric spaces of compact type. In particular, they show that if an orbit of the isotropy group is a quaternionic submanifold or a totally complex immersion, then it is a connected component of the fixed point set of a geodesic symmetry, i.e., a polar. Conversely, any polar is either a quaternionic submanifold or the image of a totally complex immersion. The results are proven by purely Lie-theoretic methods, using a computational case-by-case approach where each possible value of the rank of the symmetric space (1, 2, 3 and 4) is treated separately.