Journal of Lie Theory 17 (2007), No. 3, 505--524
Copyright Heldermann Verlag 2007
Sur la Propriété (T) Tordue par un Produit Tensoriel
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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