The classification of Boolean degree 1 functions in high-dimensional finite vector spaces

Abstract

We classify the Boolean degree 1 1 functions of k k -spaces in a vector space of dimension n n (also known as Cameron-Liebler classes) over the field with q q elements for n ≥ n 0 ( k , q ) n \geq n_0(k, q) . This also implies that two-intersecting sets with respect to k k -spaces do not exist for n ≥ n 0 ( k , q ) n \geq n_0(k, q) . Our main ingredient is the Ramsey theory for geometric lattices.