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We prove the Gan-Gross-Prasad conjecture for$\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ in generaland prove its refinement, namely the Ichino-Ikeda type explicit formula for thecentral $L$-values, under certain assumptions. Similarly, we also prove itssplit analogue, namely the Gan-Gross-Prasad conjecture and its refinement for$\left(\mathrm{GL}_{2n}, \mathrm{GL}_1\right) $ in general.

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