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

Abstract

Let G G be a reductive p \mathfrak {p} -adic group. In his paper, “The Plancherel Formula for Reductive p \mathfrak {p} -adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for G G and sketched a proof of the Plancherel theorem for G 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.