On tori periods of Weil representations of unitary groups
| Autor: | Borade, Neelima, Franzel, Jonas, Girsch, Johannes, Yao, Wei, Yu, Qiyao, Zelingher, Elad |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We determine the restriction of Weil representations of unitary groups to maximal tori. In the local case, we show that the Weil representation contains a pair of compatible characters if and only if a root number condition holds. In the global case, we show that a tori period corresponding to a maximal anisotropic torus of the global theta lift of a character does not vanish if and only if the local condition is satisfied everywhere and a central value of an $L$-function does not vanish. Our proof makes use of the seesaw argument and of the well-known theta lifting results from $\operatorname{U}\left(1\right)$ to $\operatorname{U}\left(1\right)$. Our results are used in other papers to construct Arthur packets for $G_2$. Comment: 36 pages. Comments are welcome |
| Databáze: | arXiv |
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