The space of linear anti-symplectic involutions is a homogenous space - Albers, Peter; Frauenfelder, Urs (Archiv der Mathematik, 2012)
In this note we prove that the space of linear anti-symplectic involutions is the homogenous space Gl(n,R)\Sp(n). This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem.