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 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.

This paper was previously a part of the paper arXiv:1301.1713. While arXiv:1301.1713 still contains a statement of one of the results of this paper, the proof was removed from arXiv:1301.1713 due to length considerations. 21 pages, 2 figures. Comments, questions, and/or corrections welcome