Classical Theta Lifts for Higher Metaplectic Covering Groups

Solomon Friedberg*, David Ginzburg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by using as integral kernel a theta series on the metaplectic double cover of a symplectic group that is constructed from the Weil representation. There is also an analogous local correspondence. In this work we present an extension of the classical theta correspondence to higher degree metaplectic covers of symplectic and special orthogonal groups. The key issue here is that for higher degree covers there is no analogue of the Weil representation, and additional ingredients are needed. Our work reflects a broader paradigm: constructions in automorphic forms that work for algebraic groups or their double covers should often extend to higher degree metaplectic covers.

Original languageEnglish
Pages (from-to)1531-1582
Number of pages52
JournalGeometric and Functional Analysis
Volume30
Issue number6
DOIs
StatePublished - Dec 2020

Keywords

  • Metaplectic cover
  • Theta lifting
  • Unipotent orbit
  • Weil representation

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