### Dual Blobs and Plancherel Formulas

Ju-Lee Kim (2004)

Bulletin de la Société Mathématique de France

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Let $k$ be a $p$-adic field. Let $G$ be the group of $k$-rational points of a connected reductive group $\U0001d5a6$ defined over $k$, and let $\U0001d524$ be its Lie algebra. Under certain hypotheses on $\U0001d5a6$ and $k$, wethe tempered dual $\widehat{G}$ of $G$ via the Plancherel formula on $\U0001d524$, using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on $\U0001d524$ and $G$. As a consequence, we prove that any tempered representation contains a good minimal $\U0001d5aa$-type; we extend this result to irreducible...