旋范数与λ范数

摘要：

给定一个$K$ -型$π$，已知它的自旋范数（由于第一命名的作者）由它的lambda范数（由于Vogan）下界。也就是说，$\|π\|_{\rm spin}\geq \|π\|_{\rm lambda}$。本说明旨在描述哪种$π$实际上可以具有相等性。我们把这个结果应用到回火狄拉克级数上。在实群的情形下，我们得到了在所有具有实无穷小特征标的调和模中，调和Dirac级数被划分为$\#W^1$部分.

英文摘要：

Given a $K$-type $π$, it is known that its spin norm (due to first-named author) is lower bounded by its lambda norm (due to Vogan). That is, $\|π\|_{\rm spin}\geq \|π\|_{\rm lambda}$. This note aims to describe for which $π$ one can actually have equality. We apply the result to tempered Dirac series. In the case of real groups, we obtain that the tempered Dirac series are divided into $\#W^1$ parts among all tempered modules with real infinitesimal characters.

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