Weak transfer from classical groups to general linear groups (Q6565542)

The first main goal of the paper under the review is to prove the existence of a weak transfer for all classical groups, following Arthur's argument. This result is conditional on the weighted fundamental lemma and presents a trace formula argument that discrete automorphic representations of classical groups weakly transfer to general linear groups, in the sense that the Satake parameters at finite places and infinitesimal characters at infinite places are transported via the \(L\)-morphism.\N\NThe second main goal of the paper is to prove Buzzard and Gee's conjecture on the existence of automorphic Galois representations valued in the \(C\)-groups, using the obtained weak transfer. The other key ingredient for this proof follows from the construction of automorphic Galois representations for general linear groups.