Journal of Lie Theory, Vol. 10, No. 2, pp. 255-267 (2000)

A proof of property (RD) for cocompact lattices of SL(3,R) and SL(3,C)

Vincent Lafforgue

Département de Mathématiques et Applications
Ecole Normale Supérieure
45 rue d'Ulm
75230 PARIS CEDEX 05, France

Abstract: We prove that cocompact lattices in $SL_3(\mathbb R)$ and $SL_3(\mathbb C)$ have property (RD) of Jolissaint. This property asserts that functions on these groups which are $l^2$ with some polynomial decay belong to the reduced $C^*$-algebra. Ramagge, Robertson and Steger proved the same result for cocompact lattices in $SL_3$ of $p$-adic fields and we use the same method.

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