Cameron-Liebler sets for maximal totally isotropic flats in classical 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.