Introduction Let ̃ SL(2,F) be the metaplectic two-fold cover of SL(2,F), the special linear group in two variables over a local field F of characteristic 0. The inverse image T̃ of a maximal torus T in ̃ SL(2,F) is an abelian extension of T by ±1. We consider the question of whether this extension is trivial. We exclude the case F = C, which is trivial. More generally suppose A is a subgroup of the circle T containing±1. The inclusion of ±1 in A induces a map on cohomology, and defines an… CONTINUE READING