On a conjecture of Cameron and Liebler (Q1294059)

Let \(P\) and \(L\) denote the vector spaces defined by the points and lines respectively of \(PG(3,q)\) and let \(P^*,L^*\) be the dual spaces. Let \(\alpha(P^*)=\sum_{P\in\ell}\ell^*\). Then \(\alpha\) defines a transformation from \(P^*\) to \(L^*\). The Cameron-Liebler line classes are those sets of lines whose characteristic functions are in the image of \(\alpha\). The author uses the notion of a clique to develop a connection between Cameron-Liebler classes in \(PG(3,q)\) and blocking sets in \(PG(2,q)\). From this, he gets restrictions on the parameters of the Cameron-Liebler classes. The parameters can be defined in various ways. In particular, a Cameron-Liebler class with parameter \(x\) has \(x(q^2+q+1)\) elements.