A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical (Q1288191)

Let \(G\) be a classical algebraic group over an algebraically closed field. The authors classify all instances when a parabolic subgroup \(P\) of \(G\) acts on its unipotent radical \(P_u\), or on \(\mathfrak p_u\), the Lie algebra of \(P_u\), with only a finite number of orbits, and furthermore obtain a combinatorial formula for the number of orbits in the finite cases for general linear groups.