algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety ad-nilpotent elements; Lie algebra; semisimple complex Lie group; nilpotent orbits; Weyl group; complex homology; flag variety; isotropy group; Springer's representation; primitive ideals; enveloping algebra; highest weight; irreducible representation 