COMPACTIFICATION OF PARAHERMITIAN SYMMETRIC SPACES AND ITS APPLICATIONS, II: STRATIFICATIONS AND

AUTOMORPHISM GROUPS.

SOJI KANEYUKI

Abstract. 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.