Work

On residual automorphic representations and period integrals for symplectic groups

Year: 2024

Type: preprint

Abstract: We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible component of the residual spectrum of the rank $k$ symplectic group $\mathrm{Sp}_k$ for any $k\ge 2n$. We show that this residual representation admits a non-zero $\mathrm{Sp}_n\times \mathrm{Sp}_{k-n}$-invariant linear form. This generalizes a construction of Ginzburg, Rallis and Soudry, the case $k=2n$, that arises in the descent method.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2410.10635

Authors: Friedberg, Solomon, Ginzburg, David, Offen, Omer

Institution: Boston College

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Collaborative Research: Periods and Functorial Transfer, Collaborative Research: Periods and Functorial Transfer

OpenAlex ID: W4403571120

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