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

Jacquet, Hervé; Ye, Yangbo

C. R. Acad. Sci., Paris, Sér. I 311, No. 11, 671-676 (1990).

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

MSC:

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

Keywords:

Kloosterman integrals; relative trace formula; automorphic representations; quadratic base changes; distinguished

Citations:

Zbl 0575.14004; Zbl 0665.10020