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Local-global principles for periods of automorphic forms

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Nadir Matringe

时间

2025年12月01日 10:00 至 11:00

地点

Shuangqing-B627

摘要

In a famous paper, Waldspurger proved a local-global principle for a cuspidal automorphic representation of an inner form of $GL(2)$, to support a nonvanishing toric period integral. This was generalized in two directions. The first direction is the famous global Gan-Gross-Prasad conjectures, proven in many cases, but maybe not yet for special orthogonal groups. The second, which is in a sense more natural, leads to the so-called Guo-Jacquet conjecture for automorphic representations of inner forms of $GL(n)$, so far proven under local restrictions. I will present a local-global principle for non-vanishing of period integrals attached to several symmetric subgroups of inner forms of $GL(n)$, in particular generalizing that of Waldspurger. This in particular gives a complete proof of the direct implication of the Guo-Jacquet conjecture. This work is a collaboration with Omer Offen and Chang Yang.