Shelling totally nonnegative flag varieties
| dc.creator | Williams, Lauren K. | |
| dc.date | 2005-09-06 | |
| dc.date.accessioned | 2026-07-07T05:22:59Z | |
| dc.date.available | 2026-07-07T05:22:59Z | |
| dc.description | In this paper we study the partially ordered set Q^J of cells in Rietsch's cell decomposition of the totally nonnegative part of an arbitrary flag variety P^J_{\geq 0}. Our goal is to understand the geometry of P^J_{\geq 0}: Lusztig has proved that this space is contractible, but it is unknown whether the closure of each cell is contractible, and whether P^J_{\geq 0} is homeomorphic to a ball. The order complex |Q^J| is a simplicial complex which can be thought of as a combinatorial approximation of P^J_{\geq 0}. Using combinatorial tools such as Bjorner's EL-labellings and Dyer's reflection orders, we prove that Q^J is graded, thin and EL-shellable. As a corollary, we deduce that Q^J is Eulerian and that the Euler characteristic of the closure of each cell is 1. Additionally, our results imply that |Q^J| is homeomorphic to a ball, and moreover, that Q^J is the face poset of some regular CW complex homeomorphic to a ball. | |
| dc.description | 21 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0509129 | |
| dc.identifier | http://arxiv.org/abs/math/0509129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76274 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Shelling totally nonnegative flag varieties | |
| dc.type | text |