On automorphisms of flag spaces
Algebraic Geometry
2024-02-13 v1 Representation Theory
Abstract
We show that the automorphisms of the flag space associated with a 3-dimensional projective space can be characterized as bijections preserving a certain binary relation on the set of flags in both directions. From this we derive that there are no other automorphisms of the flag space than those coming from collineations and dualities of the underlying projective space. Further, for a commutative ground field, we discuss the corresponding flag variety and characterize its group of automorphic collineations.
Cite
@article{arxiv.1304.0174,
title = {On automorphisms of flag spaces},
author = {Hans Havlicek and Klaus List and Corrado Zanella},
journal= {arXiv preprint arXiv:1304.0174},
year = {2024}
}