Bruhat order for two flags and a line

Details Bruhat order for two flags and a line Bruhat order for two flags and a line

2002-01-11

arxiv.org/abs/math/0201104v3

Mathematics

Representation Theory

36 pages. Version 2 adds an Introduction stating results in terms of S_n; and corrects typos, including in statement of move (

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Bruhat order for two flags and a line does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bruhat order for two flags and a line, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bruhat order for two flags and a line will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725739