We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in te
rms of local functorial transfers of the generic representations of the groups we consider. The existence of the local transfers follows from global generic transfers that were established earlier.
We establish the functorial transfer of generic, automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields, completing an earlier project. Our results are definitive and, in particular,
we determine the image of this transfer completely and give a number of applications.
For a cuspidal automorphic representation Pi of GL(4,A), H. Kim proved that the exterior square transfer wedge^2Pi is an isobaric automorphic representation of GL(6,A). In this paper we characterize those representations Pi for which wedge^2Pi is cuspidal.