Details

Autor(en) / Beteiligte

• Goldberg, David
• Shahidi, Freydoon

Titel

The tempered spectrum of quasi-split classical groups III: The odd orthogonal groups

Ist Teil von

• Forum mathematicum, 2014-07, Vol.26 (4), p.1029-1069

Ort / Verlag

Berlin: De Gruyter

Erscheinungsjahr

2014

Quelle

De Gruyter journals

Beschreibungen/Notizen

• We study the tempered spectrum of special orthogonal groups of odd degree over -adic fields of characteristic zero. Residues of intertwining operators for representations parabolically induced from arbitrary maximal parabolic subgroups are determined in terms of non-vanishing of weighted sums of twisted orbital integrals. This is connected with the theory of twisted endoscopy, and poles of the Langlands -functions, in particular, with the Rankin product -function between irreducible (generic) supercuspidal representations of the classical group SO ) and those of GL ). These poles are described for, any and , explicitly in terms of twisted endoscopy. Moreover, we show these poles describe precisely when a supercuspidal representation of GL ) is the local component of the transfer from a special odd orthogonal group.