Real double flag variety for the symmetric pair (U(p, p), GL_p(ℂ)) and Galois cohomology

Abstract Let G be the indefinite unitary group U ( p, p ), H ≃ GL p (ℂ) its symmetric subgroup, P S the Siegel parabolic subgroup of G , and B H a Borel subgroup of H . In this article, we give a classification of the orbit decomposition H \ ( H/B H × G/P S ) of the real double flag variety by using the Galois cohomology in the case where p = 2.