DISTINGUISHED REPRESENTATIONS OF METAPLECTIC GROUPS

We propose a conjecture that automorphic distinguished representations on n-fold covering groups of GL(nr) are parametrized by automorphic c uspidal representations of GL(r). We also give a local result on unram ified distinguished representations; noncuspidal automorphic distingui shed representations are constructed by Eisenstein series; and some ty pes of Rankin-Selberg convolutions of a metaplectic form against a dis tinguished form are shown to have Euler products.