The Howe-Moore property for real and p-adic groups
Functional Analysis
2012-02-17 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.1003.1484,
title = {The Howe-Moore property for real and p-adic groups},
author = {Raf Cluckers and Yves Cornulier and Nicolas Louvet and Romain Tessera and Alain Valette},
journal= {arXiv preprint arXiv:1003.1484},
year = {2012}
}
Comments
25 pages, no figure