Abstract
Let k be a p-adic eld. Let G be the group of k-rational points of a connected reductive group G dened over k, and let g be its Lie algebra. Under certain hypotheses on G and k, we quantify the tempered dual b G of G via the Plancherel formula on g, using some character expansions. This involves matching spectral de- composition factors of the Plancherel formulas on g and G. As a consequence, we prove that any tempered representation contains a good minimal K-type; we extend this result to irreducible admissible representations.
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