Geodesic
Bruhat order for two flags and a line
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 1, pp. 71-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $S _{ VS} n = dim( V$, but also cycles of arbitrary length. Our proofs use only elementary linear algebra and combinatorics.
Keywords: keywords quiver representations, multiple flags, degeneration, geometric order 
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     author = {Magyar, Peter},
     title = {Bruhat order for two flags and a line},
     journal = {Journal of Algebraic Combinatorics},
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     number = {1},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2005__21_1_a0/}
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Magyar, Peter. Bruhat order for two flags and a line. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 1, pp. 71-101. http://geodesic.mathdoc.fr/item/JAC_2005__21_1_a0/