2002/01/11 by Peter Magyar, Péter Magyar, Magyar, Peter
Computer Science · Mathematics · #14L35 #51N30 #Advanced Algebra and Logic #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.CO #math.RT #msc:14L35 #msc:51N30 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0201104
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
openalex publication_date 2002/01/11 · arxiv created 2003/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Sn, n=dim(V), but also cycles of arbitrary length. Our proofs use only elementary linear algebra and combinatorics.