  In this paper we continue our program of extending the methods of geometric
scattering theory to encompass the analysis of the Laplacian on symmetric
spaces of rank greater than one and their geometric perturbations. Our goal
here is to explain how analysis of the Laplacian on the globally symmetric
space $\SL(3,\RR)/\SO(3,\RR)$ is very closely related to quantum three-body
scattering. In particular, we adapt geometric constructions from recent
advances in that field by one of us (A.V.), as well as from our previous work
[Mazzeo-Vasy:Resolvents] concerning resolvents for product spaces, to give a
precise description of the resolvent and the spherical functions on this space.
Amongst the many technical advantages, these methods give results which are
uniform up to the walls of the Weyl chambers.
