algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Mumford-Tate group; automorphic cohomology; Mumford-Tate domain; CM point; homogeneous complex manifold; Lagrange quadrilateral; homogeneous line bundle; correspondence space; cycle space; Stein manifold; Penrose transform; coherent cohomology; Picard and Siegel automorphic forms; automorphic cohomology; cuspidal automorphic cohomology; discrete series; Lie algebra cohomology; K-type; TDLDS 