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Journal of Lie Theory 17 (2007), No. 3, 505--524
Copyright 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


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.

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