On $m$-ovoids of finite classical polar spaces with an irreducible transitive automorphism group

TL;DR

This paper classifies $m$-ovoids in finite classical polar spaces with irreducible transitive automorphism groups, leading to new infinite families of such structures and advancing understanding of their symmetry properties.

Contribution

It provides a classification of $m$-ovoids with irreducible transitive automorphism groups and introduces new infinite families of these objects.

Findings

Classified $m$-ovoids with irreducible transitive automorphism groups.

Discovered several new infinite families of transitive $m$-ovoids.

Enhanced understanding of symmetry in finite classical polar spaces.

Abstract

In this paper, we classify the $m$-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive $m$-ovoids.