对称性破缺微分算子与离散序列

中文摘要 AI 辅助

对于满足等秩条件的半单李群$G$，最基本的酉不可约表示族是由Harish-Chandra发现的离散序列。本文结合经典结果与T. Kobayashi、Nakahama和Pevzner的近期工作，研究离散序列限制到同类型子群$H$时对称性破缺算子的结构。我们利用表示的再生核以及先前的对偶原理，来寻找表示对称性破缺算子的微分算子的具体性质细节，特别是它们在多大程度上由$G/K$中$H$轨道的法向微分给出。

英文摘要

For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the Discrete Series found by Harish-Chandra. In this paper, we study the structure of symmetry breaking operators for Discrete Series when restricted to a subgroup $H$ of the same type by combining classical results with recent work of T. Kobayashi, Nakahama and Pevzner. This we do by using reproducing kernels for the representations and our previous duality principle in order to find some explicit details on the nature of the differential operators representing symmetry breaking operators, in particular to what extent they are given by differentiations in normal directions to the $H$-orbit in $G/K$.

发表机构

• Aarhus University（奥胡斯大学）
• FAMAF-CIEM（马拉凯-科尔多瓦大学数学与物理系计算数学中心）

机构由 AI 辅助整理，请以论文原文为准。