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

We consider the residues at the poles in the half plane R e ( 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 co...

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Bibliographic Details
Published in:Research in number theory 2022-03, Vol.8 (1), Article 10
Main Authors: Ginzburg, David, Soudry, David
Format: Article
Language:English
Subjects:
Lie groups
Mathematics
Mathematics and Statistics
Number Theory
Representations
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Summary:We consider the residues at the poles in the half plane R e ( 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.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-021-00306-5