论文标题
限制自旋（n，1）对抛物线亚组的不可还原统一表示
Restriction of irreducible unitary representations of Spin(N,1) to parabolic subgroups
论文作者
论文摘要
在本文中，我们获得了$ \ spin（n，1）$限于抛物线子组$ p $的所有不可约的单一表示法的明确分支法律。事实证明，限制是$ p $不可约的统一表示的有限直接总和。我们还验证了Duflo对抛物线亚组$ p $的$ \ spin（n，1）$ perked代表的分支定律的猜想。也就是说：在轨道法的框架中，钢化表示的分支定律取决于从相应的coadhexhinexhinexhinexhight Orbit的矩映射的行为。这项工作中使用的一些关键工具包括：傅立叶变换，knapp-stein交织操作员，卡塞尔曼·沃拉赫全球化，扎克曼翻译原理，杜克所的结果，用于半代数群体的平滑表示。
In this paper, we obtain explicit branching laws for all irreducible unitary representations of $\Spin(N,1)$ restricted to a parabolic subgroup $P$. The restriction turns out to be a finite direct sum of irreducible unitary representations of $P$. We also verify Duflo's conjecture for the branching law of tempered representations of $\Spin(N,1)$ with respect to a parabolic subgroup $P$. That is to show: in the framework of the orbit method, the branching law of a tempered representation is determined by the behavior of the moment map from the corresponding coadjoint orbit. A few key tools used in this work include: Fourier transform, Knapp-Stein intertwining operator, Casselman-Wallach globalization, Zuckerman translation principle, du Cloux's results for smooth representations of semi-algebraic groups.
