Resumen de On tori periods of Weil representations of unitary groups

Neelima Borade, Jonas Franzel, Johannes Girsch, Wei- Yao-, Qiyao Yu, Elad Zelingher

• 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 torus 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 U(1) to U(1). Our results are used in [1, 2] to construct Arthur packets for G2.