Weakly-split spherical Tits systems in quasi-reductive groups

TL;DR

This paper proves that under natural conditions, weakly-split Tits systems in quasi-reductive groups over any field are necessarily standard, extending known results to a broader class of algebraic groups.

Contribution

It establishes that weakly-split Tits systems in quasi-reductive groups are always standard, generalizing previous results beyond reductive groups.

Findings

Weakly-split Tits systems are standard in quasi-reductive groups.

The result applies over arbitrary fields.

Theorem B confirms the standard form under natural conditions.

Abstract

The main result of this paper (Theorem B) asserts that under natural conditions, any weakly-split Tits system in G(k), G a reductive or quasi-reductive group over an arbitrary field k, is the standard one.