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, [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).

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

“…Proof By [11, lemma 2.4], $${\phi }_{i}^{(2\nu )}(j)$$ is computed for all $$2\le i,j\le \nu $$. $$\square $$…”

“…Similar problems have been investigated by various researchers under different names: Boolean degree one functions, completely regular codes of strength 0 and covering radius 1, and tight sets, see [19] for more details on these connections. Recently, De Boeck et al [13, 11] studied Cameron–Liebler sets of generators in polar spaces, and D'haeseleer et al [15, 16] studied Cameron–Liebler sets in $$AG(n,q)$$. Their research stimulate us to consider Cameron–Liebler sets in classical affine spaces.…”