The Bruhat order on clans

We give an explicit description of the closure containment order (or “Bruhat order”) on the set of orbits of GL_p × GL_q on the flag variety GL_p+q/B , relative to the parametrization of the orbits by combinatorial objects called “clans”. This leads to a corresponding description of the closures of such orbits as sets of flags satisfying certain incidence conditions encoded by the parametrizing clans.