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arXiv · 2301.01004

Spin Norm and Lambda Norm

Chengyu Du·Chao-ping Dong
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Abstract

Given a $K$-type $\pi$, it is known that its spin norm (due to first-named author) is lower bounded by its lambda norm (due to Vogan). That is, $\|\pi\|_{\rm spin}\geq \|\pi\|_{\rm lambda}$. This note aims to describe for which $\pi$ 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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Chengyu Du, Chao-ping Dong. 2023-01-03. Spin Norm and Lambda Norm. https://arxiv.org/abs/2301.01004

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