A Proof of Langlands' Conjecture on Plancherel Measures; Complementary Series of -adic groups

Abstract

analysis of p-adic reductive groups. Our first result, Theorem 7.9, proves a conjecture of Langlands on normalization of intertwining operators by means of local Langlands root numbers and L-functions, at least when the group is quasi-split and the inducing representation is generic. Assuming two natural conjectures in harmonic analysis of p-adic groups, we also prove the validity of the conjecture in general (Theorem 9.5). As our second result we obtain all the complementary series and special representations of quasi-split p-adic groups coming from rank-one parabolic subgroups and generic supercuspidal represen