On the Gan–Gross–Prasad conjecture and its refinement for \(\left( \textrm{U}\left( 2n\right) , \textrm{U}\left( 1\right) \right) \)

We prove the Gan–Gross–Prasad conjecture for \(\left( \textrm{U}\left( 2n\right) , \textrm{U}\left( 1\right) \right) \) $\left(\text{U},\left(2,n\right),,,\text{U},\left(1\right)\right)$ in the general case and prove its refinement, namely the Ichino–Ikeda-type explicit formula for the central L-values, under certain assumptions. By a similar argument, we also prove its split analogue, namely the Gan–Gross–Prasad conjecture and its refinement for \(\left( \textrm{GL}_{2n}, \textrm{GL}_1\right) \) $\left({\text{GL}}_{2n},,,{\text{GL}}_1\right)$ in general.