Geometry of symmetric spaces of type EIII

TL;DR

This paper extends the understanding of the geometry of symmetric spaces of type EIII to arbitrary fields with characteristic not 2 or 3, and applies this to prove a variant of the Chain lemma for microweight tori in E6 groups.

Contribution

It generalizes Atsuyama's results on EIII symmetric spaces to broader fields and introduces a new variant of the Chain lemma for microweight tori in E6.

Findings

Extended geometric results of EIII symmetric spaces to arbitrary fields.

Proved a variant of the Chain lemma for microweight tori in E6.

Enhanced understanding of algebraic structures in symmetric spaces.

Abstract

In this paper we generalize Atsuyama result on the geometry of symmetric spaces of type EIII to the case of arbitrary fields of characteristic not 2 or 3. As an application we prove a variant of "Chain lemma" for microweight tori in groups of type E6.