Real double flag variety for the symmetric pair $(U(p,p),G{L}_p(\mathbb{C}))$ and Galois cohomology

Abstract

Let $G$ be the indefinite unitary group $U(p,p)$, $H\simeq G{L}_p(\mathbb{C})$ 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 $H\backslash (H/B_H\times G/P_S)$ of the real double flag variety by using the Galois cohomology in the case where $p=2$.

11 pages

References in corpus (2)

• Double flag varieties for a symmetric pair and finiteness of orbits
• Orbit embedding for double flag varieties and Steinberg map