English

The Bruhat order on clans

Combinatorics 2015-10-09 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1510.01900,
  title  = {The Bruhat order on clans},
  author = {Benjamin J. Wyser},
  journal= {arXiv preprint arXiv:1510.01900},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T11:14:42.236Z