Equivalent definitions for (degree one) Cameron–Liebler classes of generators in finite classical 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, De Boeck et al. (2019). . These degree one Cameron–Liebler sets are defined similar to the Boolean degree one functions, Filmus and Ihringer (2019). 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).