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 ${\mathcal{O}}_{\nu }$ 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 ${\mathcal{O}}_{\nu }$, obtain several equivalent definitions and present some classification results.

25 pages