algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety symmetric space associated to the semisimple real algebraic group; torsionfree arithmetic subgroup; locally symmetric space; Hilbert modular variety; (2n)-dimensional real hyperbolic space; \(L_ 2\)-cohomology; middle intersection homology; neighborhood of a boundary point; warped product 