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arXiv · 2412.05518

On the $\mathrm{Sp}_{2n}$-distinguished automorphic spectrum of $\mathrm{U}_{2n}$

Kewen Wang·Yu Xin
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Abstract

Given a reductive group $G$ and a reductive subgroup $H$, both defined over a number field $F$, we introduce the notion of the $H$-distinguished automorphic spectrum of $G$ and analyze it for the pair $(\mathrm{U}_{2n},\mathrm{Sp}_{2n})$. We derived a formula for period integrals of pseudo-Eisenstein series of $\mathrm{U}_{2n}$ in analogy with the main result of Lapid and Offen in their work analyzing the pair $(\mathrm{Sp}_{4n},\mathrm{Sp}_{2n} \times \mathrm{Sp}_{2n})$. We give an upper bound of the distinguished spectrum with the formula. A non-trivial lower bound of the discrete distinguished spectrum is expected from the formula, given the previous work.

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Kewen Wang, Yu Xin. 2024-12-07. On the $\mathrm{Sp}_{2n}$-distinguished automorphic spectrum of $\mathrm{U}_{2n}$. https://arxiv.org/abs/2412.05518

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