Cameron–Liebler conjecture for Boolean degree 1 functions on Grassmann graphs

Let $V=\mathbb{F}_q^n$ and let $J_q(n,k)$ be the Grassmann graph whose vertices are the $k$-dimensional subspaces of $V$. A function $f$ on the vertices is Boolean degree $1$ if it takes values in $\{0,1\}$ and is a real linear combination of the incidence functions of points and hyperplanes. Cameron–Liebler conjecture. Let $n\geq 4$ and $k=2$. If $f$ is a Boolean degree $1$ function on $J_q(n,k)$, then $f$ depends on at most one point and one hyperplane. The conjecture is disproved: many counterexamples are known when $(n,k)=(4,2)$ and $q\geq 3$.