algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety unitary representations; complex connected reductive Lie groups; indefinite symmetric space; fixed point subgroup; involution; \({\mathcal D}\)- modules; flag variety; sheaf; twisted differential operators; global sections; discrete series representation; multiplicities; microdifferential operators; irreducibility; principal series representation 