We classify the {\it Boolean degree $1$ functions} of $k$-spaces in a vector space of dimension $n$ (also known as {\it Cameron-Liebler classes}) over the field with $q$ elements for $n \geq n_0(k, q)$, a problem going back to a work by Cameron and Liebler from 1982. This also implies that two-intersecting sets with respect to $k$-spaces do not exist for $n \geq n_0(k, q)$. Our main ingredient is the Ramsey theory for geometric lattices.

翻译：我们在$q$元域上$n$维向量空间的$k$-子空间上分类了{\it 布尔度$1$函数}（也称为{\it Cameron-Liebler类}），该问题可追溯到Cameron与Liebler于1982年的工作，其中$n \geq n_0(k, q)$。这同时表明，对于$n \geq n_0(k, q)$，关于$k$-子空间的两相交集不存在。我们的主要工具是几何格上的Ramsey理论。