Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 17 (2007), No. 3, 505--524Copyright Heldermann Verlag 2007 Sur la Propriété (T) Tordue par un Produit Tensoriel Maria-Paula Gomez-Aparicio Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013 Paris, France gomez@math.jussieu.fr [Abstract-pdf] We consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a strengthening of Kazhdan's Property (T). We use the uniform decay of the matrix coefficients of unitary representations, to show that for most of the real semi-simple Lie groups having Kazhdan's Property (T), any finite dimensional irreducible representation $\rho$ of $G$, is isolated among representations of the form $\rho\otimes\pi$, where $\pi$ ranges over the irreducible unitary representations, in a sense to be made precise. Keywords: Unitary representation, matrix coefficients, K-types. MSC: 22D10, 22D12, 22E46. [ Fulltext-pdf  (284  KB)] for subscribers only.