Periods and (χ,b)-factors of cuspidal automorphic forms of metaplectic groups

Abstract

We give constraints on the existence of (χ,b)-factors in the global A-parameter of a genuine cuspidal automorphic representation σ of a metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to odd orthogonal groups. We also give a refined result that relates the invariant, first occurrence index, to non-vanishing of period integrals of residues of Eisenstein series associated to the cuspidal datum χ⊗σ. This complements our previous results for symplectic groups.