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

摘要

We consider the residues at the poles in the half plane R e ( s ) ≥ 0 documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Re(s)ge 0$$end{document} 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.