Sur la Propri�t� (T) Tordue par un Produit Tensoriel

M.-P. Gomez-Aparicio

Journal of Lie theory, Tome 17 (2007) no. 3, pp. 505-524.

Résumé

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.

Détail

Classification : 22D10, 22D12, 22E46
Mots-clés : Unitary representation, matrix coefficients, K-types