Isometric group actions on Hilbert spaces: Structure of orbits - De Cornulier, Yvan; Tessera, Romain; Valette, Alain (My University, 2008)
Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.
Keywords: affine actions; Hilbert spaces; minimal actions; nilpotent groups; REPRESENTATIONS; RIGIDITY