论文标题
上等$ \ m athbb {q} $上的散射理论 - 等级本地对称空间
Scattering theory on higher $\mathbb{Q}$-rank locally symmetric spaces
论文作者
论文摘要
1977年，Victor Guillemin发表了一篇论文，讨论了几何散射理论，在该论文中，他将Lax-Phillips散射矩阵（与尖尖的非脉冲双曲表面相关联）和与一组与无限属于Infinity的地理学相关的居住时间。这项工作后来扩展到$ \ Mathbb {Q} $ - 排名一个本地对称空间，来自Lizhen Ji和Maciej Zworski的Semimple Lie Groups。在这里，我们将把上述一些结果扩展到较高的本地对称空间，特别是我们将引入更高的尺寸类似物的散射地理学类似物，称为$ \ textbf {散射flat} $，并研究这些公寓，并在局部对称的空间中使用商$ sl（3，\ mathbb {z} z} s rash s rassssssss \ s rans callase s sl（3，\ mathbb {z）所以（3）$。讨论了有关此类散射公寓以及相关的矢量参数（与Sojourn Times具有相似性）的参数化空间，称为$ \ textbf {sojourn vector} $，这些与相关的散射室友的振荡频率有关，这些散射室里来自最小的寄生虫子组来自$ \ text $ \ text $ \ sl}（sl}（3）（r）{3;关键技术是高级散射矩阵的分解。
In 1977, Victor Guillemin published a paper discussing geometric scattering theory, in which he related the Lax-Phillips Scattering matrices (associated to a noncompact hyperbolic surface with cusps) and the sojourn times associated to a set of geodesics which run to infinity in either direction. This work was later extended to $\mathbb{Q}$-rank one Locally symmetric spaces coming from Semisimple Lie groups by Lizhen Ji and Maciej Zworski. Here, we will extend some of the above mentioned results to higher rank locally symmetric spaces, in particular we will introduce higher dimensional analogues of scattering geodesics called $\textbf{Scattering Flat}$ and study these flats in the case of the locally symmetric space given by the quotient $SL(3,\mathbb{Z}) \backslash SL(3,\mathbb{R}) / SO(3)$. A parametrization space is discussed for such scattering flats as well as an associated vector valued parameter (bearing similarities to sojourn times) called $\textbf{sojourn vector}$ and these are related to the frequency of oscillations of the associated scattering matrices coming from the minimal parabolic subgroups of $\text{SL}(3,\mathbb{R})$. The key technique is the factorization of higher rank scattering matrices.
