**
Journal of Lie Theory, Vol. 10, No. 1, pp. 93-105 (2000)
**

#
On Kazhdan's property (T) and Kazhdan constants associated to a Laplacian for SL(3,R)

##
M. E. B. Bekka and M. Mayer

M. E. B. Bekka

Université de Metz

Ile du Saulcy

57045 Metz Cedex 01

bekka@poncelet.univ-metz.fr

and

Matthias Mayer

Zentrum Mathematik

Technische Universität München

D-80290 München

mayerm@mathematik.tu-muenchen.de

**Abstract:** The first purpose of this paper is to give a very elementary proof of Property (T) for SL$_{\Bbb R}(3,\kk)$ over any local field $\kk$. Here we use a modification of an argument due to Burger. The second approach to Property (T) is based on spectral properties of a Laplacian in the enveloping algebra. It is shown that for a connected Lie group $G$ Property (T) can be characterized by a spectral property of a Laplacian on the space of smooth $K$-finite vectors, where $K$ is a compact subgroup of $G$.

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2000--2001 ELibM for
the EMIS Electronic Edition
*