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.
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