论文标题
在Helgason-Johnson上
On the Helgason-Johnson bound
论文作者
论文摘要
令$ g $为一个简单的非紧凑线性谎言组。让$π$为$ g $的任何不可约的单一表示，而无限字符$λ$，其连续部分为$ν$。 1969年，美丽的Helgason-Jonson绑定说，$ν$的规范是$ρ（g）$的上限，这代表了$ g $的正根的半和。当前的论文旨在为$π$提供无限维度时的框架，以增强Helgason-Johnson的约束。我们为特殊的谎言组有明确的结果。证明的成分包括Parathasarathy的Dirac操作员不平等，Vogan铅笔以及Salamanca-Riba和Vogan引入的单位凸面船体。
Let $G$ be a simple non-compact linear Lie group. Let $π$ be any irreducible unitary representation of $G$ with infinitesimal character $Λ$ whose continuous part is $ν$. The beautiful Helgason-Jonson bound in 1969 says that the norm of $ν$ is upper bounded by the norm of $ρ(G)$, which stands for the half sum of the positive roots of $G$. The current paper aims to give a framework to sharpen the Helgason-Johnson bound when $π$ is infinite-dimensional. We have explicit results for exceptional Lie groups. Ingredients of the proof include Parathasarathy's Dirac operator inequality, Vogan pencil, and the unitarily small convex hull introduced by Salamanca-Riba and Vogan.
