Valette, Alain

2014, Jolissaint, Pierre-Nicolas, Valette, Alain

2011, Cluckers, Raf, Cornulier, Yves, Louvet, Nicolas, Tessera, Romain, Valette, Alain

We consider in this paper a relative version of the Howe-Moore property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear Lie groups or $p$-adic Lie groups, the pairs with the relative Howe-Moore property with respect to a closed, normal subgroup. This involves, in one direction, structural results on locally compact groups all of whose proper closed characteristic subgroups are compact, and, in the other direction, some results about the vanishing at infinity of oscillatory integrals.

2008, Valette, Alain

2008, Bekka, Bachir, Valette, Alain, De La Harpe, Pierre

2014, Petersen, Henrik Densing, Valette, Alain

2010, Austin, Tim, Naor, Assaf, Valette, Alain

2008, Valette, Alain, Cowling, Michael, Kashiwara, Masaki, Vogan, David A, Frenkel, Edward, Valette, Alain, Wallach, Nolan R

2012, Fernós, Talia, Valette, Alain, Martin, Florian

2009, Goulnara, Arzhantseva, Valette, Alain

2008, De Cornulier, Yvan, Tessera, Romain, Valette, Alain

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.