Bruhat order for two flags and a line
| dc.creator | Magyar, Peter | |
| dc.date | 2002-01-11 | |
| dc.date | 2003-10-13 | |
| dc.date.accessioned | 2026-07-07T04:45:49Z | |
| dc.date.available | 2026-07-07T04:45:49Z | |
| dc.description | The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a linear space V under linear transformations of V; or equivalently, it describes the closure of an orbit of GL(V) acting diagonally on the product of two flag varieties. We consider the degenerations of a triple consisting of two flags and a line, or equivalently the closure of an orbit of GL(V) acting diagonally on the product of two flag varieties and a projective space. We give a simple rank criterion to decide whether one triple can degenerate to another. We also classify the minimal degenerations, which involve not only reflections (i.e., transpositions) in the Weyl group S_n, n=dim(V), but also cycles of arbitrary length. Our proofs use only elementary linear algebra and combinatorics. | |
| dc.description | 36 pages. Version 2 adds an Introduction stating results in terms of S_n; and corrects typos, including in statement of move (v). Version 3: typos | |
| dc.identifier | https://arxiv.org/abs/math/0201104 | |
| dc.identifier | http://arxiv.org/abs/math/0201104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63099 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 14L35; 51N30 | |
| dc.title | Bruhat order for two flags and a line | |
| dc.type | text |