Valette, Alain

2014, Jolissaint, Pierre-Nicolas, Valette, Alain

2012, Cornulier, Yves, Stalder, Yves, Valette, Alain

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

Our main result is that the simple Lie group G = Sp( n; 1) acts metrically properly isometrically on L-p( G) if p > 4 n + 2. To prove this, we introduce Property (BP0V), with V being a Banach space: a locally compact group G has Property (BP0V) if every affine isometric action of G on V, such that the linear part is a C-0- representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic groups over a local field of characteristic zero, have Property ( BP V 0). As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology with respect to the left regular representation on L-2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L-2- Betti number is nonzero.

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.

2014, Petersen, Henrik Densing, 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

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

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

2008, De Cornulier, Yves, Stalder, Yves, Valette, Alain

Given a finite group H and a free group F-n, we prove that the wreath product H (sic) F-n admits a metrically proper, isometric action on a Hilbert space.