algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety reductive connected algebraic group; unipotent element; irreducible components; variety of Borel subgroups; irreducible representations; permutation representation; Levi decomposition; irreducible cuspidal representation; Coxeter group; generalized Springer correspondence; special orthogonal groups; intersection cohomology 