论文标题
delorme在两个和三维双曲空间上均相矢量束的相互交织条件
Delorme's intertwining conditions for sections of homogeneous vector bundles on two and three dimensional hyperbolic spaces
论文作者
论文摘要
半简单的谎言组$ g $在紧凑型光滑功能上的paley-fiener空间$ c^\ infty_c（g）$的描述涉及某些难以处理的互换条件。在本文中，我们使它们完全明确说明$ g = \ mathbf {sl}（2，\ mathbb {r}）^d $（$ d \ in \ mathbb {n} $）和$ g = \ g = \ mathbf {sl}（2，2，\ m athbb {c}）$。我们的结果基于对佩奇的空间的定义标准，该标准适用于一般等级的一般群体，我们来自Delorme的佩奇定理证明。在即将发表的论文中，我们将展示如何使用这些结果来研究均质矢量束之间不变差分运算符在相应的对称空间上的可溶性。
The description of the Paley-Wiener space for compactly supported smooth functions $C^\infty_c(G)$ on a semi-simple Lie group $G$ involves certain intertwining conditions that are difficult to handle. In the present paper, we make them completely explicit for $G=\mathbf{SL}(2,\mathbb{R})^d$ ($d\in \mathbb{N}$) and $G=\mathbf{SL}(2,\mathbb{C})$. Our results are based on a defining criterion for the Paley-Wiener space, valid for general groups of real rank one, that we derive from Delorme's proof of the Paley-Wiener theorem. In a forthcoming paper, we will show how these results can be used to study solvability of invariant differential operators between sections of homogeneous vector bundles over the corresponding symmetric spaces.
