Une remarque sur le changement de base quadratique. (A remark on the quadratic base change). (French) Zbl 0715.11026

We conjecture that automorphic representations of GL(m) which are quadratic base changes are characterized by the property of being distinguished [cf. G. Harder, R. P. Langlands and M. Rapoport, J. Reine Angew. Math. 366, 53-120 (1986; Zbl 0575.14004)] with respect to a quasi-split unitary group. We state a more precise form of this conjecture and prove it in the case \(m=2\) with the methods of the second author [J. Reine Angew. Math. 400, 57-121 (1989; Zbl 0665.10020)].
Reviewer: Ye Yangbo


11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings