On flips of unitary buildings I: Classification of flips

TL;DR

This paper classifies flips of buildings derived from non-degenerate unitary spaces over finite fields of odd characteristic, analyzing their actions and constructing related geometries with flag transitivity.

Contribution

It provides a classification of flips in unitary buildings and constructs geometries demonstrating flag transitivity, advancing understanding of these symmetries.

Findings

Classification of flips based on their action on vector spaces

Construction of geometries related to flips

Proof of flag transitivity of these geometries

Abstract

We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related to flips and prove that these geometries are flag transitive.