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Scattering theory on SL(3)/SO(3): Connections with quantum 3‐body scattering
Author(s) -
Mazzeo Rafe,
Vasy András
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl004
Subject(s) - mathematics , resolvent , laplace operator , scattering , quantum , space (punctuation) , pure mathematics , scattering theory , field (mathematics) , product (mathematics) , rank (graph theory) , quantum field theory , vector space , theoretical physics , mathematical analysis , geometry , quantum mechanics , physics , mathematical physics , combinatorics , computer science , operating system
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.