Journal of Lie Theory

no. 3
Sur la Propriété (T) Tordue par un Produit Tensoriel
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 505-524
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.
DOI: 10.5802/jolt.458
Classification: 22D10, 22D12, 22E46
Keywords: Unitary representation, matrix coefficients, K-types 
@article{JOLT_2007_17_3_a3,
     author = {M.-P. Gomez-Aparicio},
     title = {Sur la {Propri\'et\'e} {(T)} {Tordue} par un {Produit} {Tensoriel}},
     journal = {Journal of Lie Theory},
     pages = {505--524},
     year = {2007},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.458},
     zbl = {1132.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.458/}
}
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M.-P. Gomez-Aparicio. Sur la Propriété (T) Tordue par un Produit Tensoriel. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 505-524. doi: 10.5802/jolt.458

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