Sur la Propriété (T) tordue par un produit tensoriel

Details Sur la Propriété (T) tordue par un produit tensoriel Sur la Propriété (T) tordue par un produit tensoriel

2006-05-16

arxiv.org/abs/math/0605450v2

Mathematics

Representation Theory

This is a revised version, 21 pages, to appear in Journal of Lie Theory

Scientific paper

In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting 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.

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