Periods and $(\chi ,b)$-factors of Cuspidal Automorphic Forms of Metaplectic Groups

Abstract

We give constraints on the existence of $(\chi ,b)$-factors in the global $A$-parameter of a genuine cuspidal automorphic representation $\sigma$ 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 $\chi \otimes \sigma$. This complements our previous results for symplectic groups.

35 pages. Clarifies the $L$-function for metaplectic group used. See Remark 2.2

References in corpus (1)

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups