DISTINGUISHED REPRESENTATIONS FOR THE ORTHOGONAL GROUP

We reeaxim earlier work (which is itself a reexamination of Waldspurger's work) to show that automorphic representations of GL (2) which correspond to automorphic representations of the two fold cover of GL (2) are distinguished, in a suitable sense, with respect to an orthogonal group, which, furthermore, can be taken to be split. The motivation for this Note is to emphasize the role of the various forms of the orthogonal group and to suggest a generalization to GL (m).