The algebra of invariants of the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra

In the paper the algebra of invariants of the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We set up a conjecture on the structure of the algebra of invariants. The conjecture is proved for parabolic subalgebras of special types.