Bruhat Order for Two Flags and a Line
نویسنده
چکیده
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 involve only elementary linear algebra and combinatorics
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