# A proof of Langlands' conjecture on Plancherel measures; Complementary series for p-adic groups

**Freydoon Shahidi**

CiteWeb id: 20160000090

CiteWeb score: 450

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

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