Year: 2012
Type: article
Abstract: . We study the tempered spectrum of special orthogonal groups of odd degree over p-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 L-functions, in particular, with the Rankin product L-function between irreducible (generic) supercuspidal representations of the classical group SO2m+1(F) and those of GLk(F). These poles are described for, any m and k, explicitly in terms of twisted endoscopy. Moreover, we show these poles describe precisely when a supercuspidal representation of GLk(F) is the local component of the transfer from a special odd orthogonal group.
Source: Forum Mathematicum
Authors: David Goldberg, Freydoon Shahidi
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2024750188