Linear conditions imposed on flag varieties

Details Linear conditions imposed on flag varieties Linear conditions imposed on flag varieties

2004-06-26

arxiv.org/abs/math/0406541v3

Mathematics

Algebraic Geometry

16 pages; v2 and v3 contain editorial revisions and acknowledgements

Scientific paper

We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GL_n(C) and show that they have no odd-dimensional homology. We provide an explicit geometric construction which partitions each Hessenberg variety into pieces homeomorphic to affine space. We characterize these affine pieces by fillings of Young tableaux and show that the dimension of the affine piece can be computed by combinatorial rules generalizing the Eulerian numbers. We give an equivalent formulation of this result in terms of roots. We conclude with a section on open questions.

Affiliated with

Also associated with

No associations

Rating

Linear conditions imposed on flag varieties 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 Linear conditions imposed on flag varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear conditions imposed on flag varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-706471