The Bruhat order on clans

Abstract

We give an explicit description of the closure containment order (or "Bruhat order") on the set of orbits of $$GL_p \times GL_q$$GLp×GLq on the flag variety $$GL_{p+q}/B$$GLp+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.