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arXiv · 2410.10635

On residual automorphic representations and period integrals for symplectic groups

Solomon Friedberg·David Ginzburg·Omer Offen
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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.

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Solomon Friedberg, David Ginzburg, Omer Offen. 2024-10-14. On residual automorphic representations and period integrals for symplectic groups. https://arxiv.org/abs/2410.10635

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