# Equivalent definitions for (degree one) Cameron-Liebler classes of generators in finite classical polar spaces

## TL;DR

This paper investigates degree one Cameron-Liebler sets of generators in finite classical polar spaces, providing equivalent definitions and classifying these sets specifically in the polar spaces W(5,q) and Q(6,q).

## Contribution

It offers a comprehensive summary of equivalent definitions and a classification of degree one Cameron-Liebler sets in specific finite polar spaces, extending understanding of their structure.

## Key findings

- Equivalent definitions for degree one Cameron-Liebler sets
- Classification results for W(5,q) and Q(6,q) polar spaces
- Insights into Boolean degree one functions in polar spaces

## Abstract

In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets are defined similar to the Boolean degree one functions, [15]. We summarize the equivalent definitions for these sets and give a classification result for the degree one Cameron-Liebler sets in the polar spaces W(5,q) and Q(6,q).