The Jacquet Langlands correspondence via twisted descent

Abstract

The existence of the well-known Jacquet-Langlands correspondence was established by Jacquet and Langlands via the trace formula method in 1970. An explicit construction of such a correspondence was obtained by Shimizu via theta series in 1972. In this paper, we extend the automorphic descent method of Ginzburg-Rallis-Soudry to a new setting. As a consequence, we recover the classical Jacquet-Langlands correspondence for PGL(2) via a new explicit construction.

Final version. 30 pages. Minor revisions. To appear in Int. Math. Res. Notices

References in corpus (2)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Arthur Parameters and Cuspidal Automorphic Modules of Classical Groups