Canad. J. Math. 60(2008), 1001-1009
Printed: Oct 2008
Yves de Cornulier
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.
affine actions, Hilbert spaces, minimal actions, nilpotent groups
22D10 - Unitary representations of locally compact groups
43A35 - Positive definite functions on groups, semigroups, etc.
20F69 - Asymptotic properties of groups