Bruhat Order for Two Flags and a Line
- Peter Magyar
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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.
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- Bruhat Order for Two Flags and a Line
Journal of Algebraic Combinatorics
Volume 21, Issue 1 , pp 71-101
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- quiver representations
- multiple flags
- geometric order
- Peter Magyar (1)
- Author Affiliations
- 1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824