Split buildings of type F4 in buildings of type E6
Combinatorics
2020-01-13 v1
Abstract
A symplectic polarity of a building {\Delta} of type E6 is a polarity whose fixed point structure is a building of type F4 containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type F4). In this paper, we show in a geometric way that every building of type E6 contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type F4 fully embedded in the natural point-line geometry of {\Delta} arises from a symplectic polarity.
Keywords
Cite
@article{arxiv.2001.03399,
title = {Split buildings of type F4 in buildings of type E6},
author = {Anneleen De Schepper and N. S. Narasimha Sastry and Hendrik Van Maldeghem},
journal= {arXiv preprint arXiv:2001.03399},
year = {2020}
}
Comments
64 pages