SL（3）/ SO（3）的散射理论：与量子三体散射的联系
Scattering Theory on SL(3)/SO(3): Connections with Quantum 3-Body Scattering
摘要：
在本文中，我们继续我们的程序扩展的几何散射理论的方法，包括分析的拉普拉斯算子的对称空间的秩大于1和他们的几何扰动。我们的目标是解释如何在全球对称空间$\SL(3,\RR)/\SO(3,\RR)$的拉普拉斯分析是非常密切相关的量子三体散射。特别是，我们适应尺规作图法，从最近的进展，在该领域的一个我们（A. V.），以及从我们以前的工作[Mazzeo-Vasy：Resolvents]关于预解的积空间，给一个精确的描述的预解和球面函数在这个空间。在许多技术优势中，这些方法给出的结果直到外尔室的壁都是一致的。
英文摘要：
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.
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