Geodesic
Compactification of Parahermitian Symmetric Spaces and its Applications. II: Stratifications and Automorphism Groups
Journal of Lie theory, Tome 13 (2003) no. 2, pp. 535-563.

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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. 
@article{JLT_2003_13_2_JLT_2003_13_2_a13,
     author = {S. Kaneyuki },
     title = {Compactification of {Parahermitian} {Symmetric} {Spaces} and its {Applications.} {II:} {Stratifications} and {Automorphism} {Groups}},
     journal = {Journal of Lie theory},
     pages = {535--563},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2003},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a13/}
}
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S. Kaneyuki . Compactification of Parahermitian Symmetric Spaces and its Applications. II: Stratifications and Automorphism Groups. Journal of Lie theory, Tome 13 (2003) no. 2, pp. 535-563. http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a13/