Bruhat order for two subspaces and a flag
Representation Theory
2007-05-23 v1 Algebraic Geometry
Combinatorics
Abstract
The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a finite-dimensional vector space V; or, equivalently, the closure of an orbit of the group GL(V) acting on the direct product of two full flag varieties. We obtain a similar result for triples consisting of two subspaces and a partial flag in V; this is equivalent to describing the closure of a GL(V)-orbit in the product of two Grassmannians and one flag variety. We give a rank criterion to check whether such a triple can be degenerated to another one, and we classify the minimal degenerations. Our methods involve only elementary linear algebra and combinatorics of graphs (originating in Auslander-Reiten quivers).
Cite
@article{arxiv.0704.3061,
title = {Bruhat order for two subspaces and a flag},
author = {Evgeny Smirnov},
journal= {arXiv preprint arXiv:0704.3061},
year = {2007}
}