On the tempered spectrum of quasi-split classical groups. II (Q2715670)

Let \(F\) denote a \(p\)-adic field of characteristic zero, and let \(G\) denote the group of \(F\)-points of a quasisplit classical group defined over \(F\). In Part I of this paper [Duke Math. J. 92, 255-294 (1998; Zbl 0938.22014)], the authors determined an important part of the tempered spectrum of \(G\) when \(G\) is a symplectic or special orthogonal group. In particular, they determined the reducibility of the representations that are induced from supercuspidal representations of maximal parabolic subgroups whose Levi factors have the form \(GL_n(F)\times \widetilde{G}\), where \(\widetilde{G}\) is a classical group of the same type as \(G\) but of smaller rank. (See the review of the earlier paper for more on the context of this result.) NEWLINENEWLINENEWLINEIn the present paper, the authors solve part of the analogous problem when \(G\) is a quasisplit unitary group. Specifically, suppose that \(G\) is defined by a quadratic extension \(E/F\). Then they treat the case where the Levi factor is \(GL_n(E)\times U_m(F)\), and \(m\equiv n \bmod 2\). One difference this time is that what they call the ``singular'' term of the residue of the standard intertwining operator now has a simpler formula, and they remark that the analogous formula in their earlier paper may be simplified in a similar way. NEWLINENEWLINENEWLINEAs in their earlier article, the authors show how their results are related to the theory of twisted endoscopy.