Bruhat order for two flags and a line
摘要
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.
引用
@article{arxiv.math/0201104,
title = {Bruhat order for two flags and a line},
author = {Peter Magyar},
journal= {arXiv preprint arXiv:math/0201104},
year = {2007}
}
备注
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