On the B-canonical splittings of flag varieties
Algebraic Geometry
2010-05-26 v3 Representation Theory
Abstract
Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic. In this note, we show that an irreducible closed subvariety of the flag variety of G is compatibly split by the unique canonical Frobenius splitting if and only if it is a Richardson variety, i.e. an intersection of a Schubert and an opposite Schubert variety.
Keywords
Cite
@article{arxiv.0908.4354,
title = {On the B-canonical splittings of flag varieties},
author = {Chuck Hague},
journal= {arXiv preprint arXiv:0908.4354},
year = {2010}
}
Comments
After obtaining this result, I was informed that Allen Knutson has also recently obtained a similar result. This version fixes an error in Lemma 2.7. To appear in J. Algebra