Compactification of parahermitian symmetric spaces and its applications, II: Stratifications and automorphism groups.

Soji Kaneyuki

A simple parahermitian symmetric space is a symplectic symmetric space of a simple Lie group $G$ with two invariant Lagrangian foliations. Such a symmetric space has a nice $G$-equivariant compactification. In this paper, we obtain the stratification of the compactification, whose strata are $G$-orbits. By using this, we determine the automorphism group of the double foliation for each simple parahermitian symmetric space.