Harish-Chandra’s Plancherel theorem for 𝔭-adic groups

Silberger, Allan

doi:10.1090/S0002-9947-96-01700-X

Harish-Chandra’s Plancherel theorem for $\frak p$-adic groups
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by Allan J. Silberger

Trans. Amer. Math. Soc. 348 (1996), 4673-4686

DOI: https://doi.org/10.1090/S0002-9947-96-01700-X

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Erratum: Trans. Amer. Math. Soc. 352 (2000), 1947-1949.

Abstract:

Let $G$ be a reductive $\mathfrak {p}$-adic group. In his paper, “The Plancherel Formula for Reductive $\mathfrak {p}$-adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for $G$ and sketched a proof of the Plancherel theorem for $G$. One step in the proof, stated as Theorem 11 in Harish-Chandra’s paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.

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