
Journal of Lie Theory 17 (2007), No. 3, 505524 Copyright Heldermann Verlag 2007 Sur la Propriété (T) Tordue par un Produit Tensoriel MariaPaula GomezAparicio Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013 Paris, France gomez@math.jussieu.fr [Abstractpdf] We consider tensor products of unitary representations by irreducible nonunitary 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 semisimple 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, Ktypes. MSC: 22D10, 22D12, 22E46. [ Fulltextpdf (284 KB)] for subscribers only. 