A New Proof to the Period Problems of GL(2)

Abstract

We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global $D^{\times }(F)-$distinguished representations ${\pi }^D$ of $D^{\times }(E),$ where $D^{\times }$ is an inner form of $G{L}_2$ defined over a nonarchimedean field or a number field $F.$

Rewrite the proof in this version. arXiv admin note: text overlap with arXiv:1006.3367 by other authors

References in corpus (4)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• A `relative' local Langlands correspondence
• Theta correspondences for GSp(4)
• The Howe duality conjecture: quaternionic case

Cited by in corpus (1)

• The Prasad conjectures for $\mathrm{GS}{\mathrm{p}}_4$ and $\mathrm{PGS}{\mathrm{p}}_4$