Regular N-orbits in the nilradical of a parabolic subalgebra
  In the present paper the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We set up general conjectures on the construction of the field of invariants and the structure of orbits of maximal dimension. The conjecture is proved for parabolic subalgebras of special types. 
A. N. Panov and Victoria Sevostyanova
math.RT