Rationality of singularities and the Gorenstein property for nilpotent orbits (Q1178112)

The author essentially proves two results. First he describes the nilpotent orbits of a semisimple Lie algebra over an algebraically closed field of characteristic zero, which have the Gorenstein property. --- Secondly he considers a certain normal algebraic variety \(X\). He obtains a necessary and sufficient condition for the existence of resolvable rational singularities on \(X\) in function of the dual Grothendieck sheaf of \(X\).