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arXiv · 1305.0480

Quasi-regular representations and property RD

Adrien Boyer
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Abstract

We study \emph{property RD} in terms of rapid decay of matrix coefficients. We give new formulations of property RD in terms of a $L^{1}$-integra\-bility condition of a Banach representation. Combining this new definition with the existence of cyclic subgroups of exponential growth in non-uniform lattices in semisimple Lie groups, we deduce that there exist matrix coefficients associated to several kinds of quasi-regular representations which satisfy a "non-RD condition" for non-uniform lattices. We obtain also that such coefficients can not satisfy \emph{the weak inequality} of Harish-Chandra.

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Adrien Boyer. 2013-05-02. Quasi-regular representations and property RD. https://arxiv.org/abs/1305.0480

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