Cameron-Liebler sets for maximal totally isotropic flats in classical affine spaces

TL;DR

This paper studies Cameron-Liebler sets within the set of maximal totally isotropic flats in classical affine spaces, providing new definitions and classification results for these combinatorial structures.

Contribution

It introduces multiple equivalent definitions of Cameron-Liebler sets in this context and offers initial classification results, advancing understanding of their structure.

Findings

Multiple equivalent definitions of Cameron-Liebler sets established

Classification results for Cameron-Liebler sets obtained

Enhanced understanding of isotropic flats in affine spaces

Abstract

Let $ACG(2\nu,\mathbb{F}_q)$ be the $2\nu$-dimensional classical affine space with parameter $e$ over a $q$-element finite field $\mathbb{F}_q$, and ${\cal O}_{\nu}$ be the set of all maximal totally isotropic flats in $ACG(2\nu,\mathbb{F}_q)$. In this paper, we discuss Cameron-Liebler sets in ${\cal O}_{\nu}$, obtain several equivalent definitions and present some classification results.