Cameron-Liebler line classes of ${\rm PG}(3,q)$ admitting ${\rm PGL}(2,q)$

TL;DR

This paper introduces an infinite family of Cameron-Liebler line classes in projective 3-space with specific parameters, featuring automorphism group properties and distinctness from known families for certain q values.

Contribution

It constructs a new infinite family of Cameron-Liebler line classes with automorphism group PGL(2,q), expanding the known classifications for these geometric objects.

Findings

The family exists for q ≡ 1 mod 4.

It admits PGL(2,q) as an automorphism group.

It is not isomorphic to known families for q ≥ 9.

Abstract

In this paper we describe an infinite family of Cameron-Liebler line classes of ${\rm PG}(3,q)$ with parameter $(q^2 + 1)/2$, $q\equiv 1\pmod{4}$. The example obtained admits ${\rm PGL}(2,q)$ as an automorphism group and it is shown to be isomorphic to none of the infinite families known so far whenever $q \ge 9$.