2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124406In 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 $ρ$ of $G$, is isolated among representations of the form $ρ\otimesπ$, where $π$ ranges over the irreducible unitary representations, in a sense to be made precise.This is a revised version, 21 pages, to appear in Journal of Lie TheoryRepresentation TheoryOperator Algebras22D10; 22D12text