Image of functoriality for general spin groups

Abstract

We give a complete description of the image of the endoscopic functorial transfer of generic automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields. This result is not covered by the recent work of Arthur on endoscopic classification of automorphic representations of classical groups. The image is expected to be the same for the whole tempered spectrum, whether generic or not, once the transfer for all tempered representations is proved. We give a number of applications including estimates toward the Ramanujan conjecture for the groups involved and the characterization of automorphic representations of GL(6) which are exterior square transfers from GL(4), among others. More applications to reducibility questions for the local induced representations of p-adic groups will also follow.