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

Spin Norm and Lambda Norm