Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

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Abstract

We consider the residues at the poles in the half plane Re(s) ≥ 0 of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

Original languageEnglish
Article number10
JournalResearch in Number Theory
Volume8
Issue number1
DOIs
StatePublished - Mar 2022

Keywords

  • Eisenstein series
  • Nilpotent orbits
  • Poles
  • Speh representations

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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