Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Boyer, Adrien
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1497868218