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Proceedings of the London Mathematical Society Advance Access originally published online on December 5, 2006
Proceedings of the London Mathematical Society 2007 94(3):545-593; doi:10.1112/plms/pdl004
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© 2006 London Mathematical Society

Scattering theory on SL(3)/SO(3): connections with quantum 3-body scattering

Rafe Mazzeo1 and András Vasy2

1 Department of Mathematics
Stanford University
Stanford, CA 94305
USA
mazzeo{at}math.stanford.edu
2 Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
USA
andras{at}math.mit.edu

Received 16 October 2004. Revision received 29 March 2006.

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 1 and their geometric perturbations. Our goal here is to explain how analysis of the Laplacian on the globally symmetric space SL(3, R)/SO(3, R) 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 a previous paper of ours 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.


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