Groups of Projectivities in Spherical Buildings of Non-Simply Laced Type

TL;DR

This paper characterizes the structure and actions of projectivity groups in certain spherical buildings, providing insights into Levi subgroups of Lie type groups for buildings of types B, C, and F4.

Contribution

It describes the general and special projectivity groups for all residues of thick, irreducible spherical buildings of specified types and ranks, clarifying their structure and actions.

Findings

Determined the structure of projectivity groups in buildings of types B, C, and F4.

Established the action of these groups on residues.

Connected the findings to Levi subgroups of Lie type groups.

Abstract

In this article we describe the general and special projectivity groups for all irreducible residues of all thick, irreducible, spherical buildings of type $ \mathsf{B_{n}}$, $ \mathsf{C_{n}}$ and $\mathsf{F_4}$, and rank at least 3. This determines the exact structure and action of Levi subgroups of parabolic subgroups of groups of Lie type related to those buildings.