Regular sets of lines in rank 3 polar spaces

Abstract

There are 6 families of finite polar spaces of rank 3. The set of lines in a rank 3 polar space forms a rank 5 association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some interesting examples. We also give a new family of Cameron–Liebler sets of generators in the polar spaces $O^{+}(10,q)$ when $q=3^h$ using a regular set of lines in $O(7,q)$.