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La formule de Plancherel pour les groupes \(p\)-adiques [d’après Harish-Chandra]. (The Plancherel formula for \(p\)-adic groups [after Harish-Chandra]). (French) Zbl 1029.22016
Harish-Chandra stated the Plancherel theorem for reductive p-adic groups and sketched a proof in an article that was first published in the Collected Papers (vol. IV (1970-1983), p. 353-370 (1984; Zbl 0546.01013)]. In the present article Waldspurger gives a complete proof of the theorem based on unpublished hand-written notes by Harish-Chandra. The proof given by Waldspurger is essentially Harish-Chandra’s. New is the treatment (definition, rational continuation) of intertwining operators and its application in the study of the constant term. The Eisenstein integral disappeared (it can be, and is, replaced by coefficients of induced representations). The notations have been modernized. There exists another proof for this Plancherel theorem by A. Silberger [Trans. Am. Math. Soc. 348, 4673-4686 (1996; Zbl 0869.22007) and 352, 1947-1949 (1999)]. The author of the present article expects, as he says in the introduction, that his text is not a double to Silberger’s article and that it will shed a different light on certain points. This is certainly the case.

MSC:
22E35 Analysis on \(p\)-adic Lie groups
22E50 Representations of Lie and linear algebraic groups over local fields
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