Base change for ≈ SL2

Abstract

Solvable base change for the metaplectic group ≈ SL 2 over both local and global fields in studied. The method is to use Waldspurger's correspondence to relate base change for ≈ SL 2 to base change for PGL 2. In the global case there are certain cuspidal representations which “disappear” under a quadratic base change. They then “reappear” under any subsequent quadratic base change. Such a phenomenon never occurs for PGL 2.