Refined global Gan–Gross–Prasad conjecture for Bessel periods

Abstract

Abstract We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. N. Harris in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain L-function. To support such conjecture, we provide two examples for pairs SO 5 × SO 2 $\operatorname{SO}_{5}\times\operatorname{SO}_{2}$ and SO 6 × SO 3 $\operatorname{SO}_{6}\times\operatorname{SO}_{3}$ (both co-rank 3) in the endoscopic case via theta lifting.