Compositio Mathematica

Principe de densité pour les groupes réductifs

a1 U.F.R. de mathématiques, Université Denis Diderot, 2 place Jussieu, F-75251 Paris Cedex 05; e-mail:

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The main goal of this Letter is to give a new proof of a result conjectured by D. De George and N. Wallach and proved by P. Delorme and to extend it to the $S$-arithmetic setting. The proof is based on a density principle.

Key Words: Reductive groups; Paley-Wiener theorem; (limit) multiplicities; Hecke algebra; generic irreducibility; co-compact discrete subgroups; trace formula; Plancherel measure.