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

Abstract

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

56 pages. Revised extensively following the suggestions by the referee. Appeared online in Mathematische Annalen

References in corpus (3)

• La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes unitaires
• Irreducibility of Theta Lifting for Unitary Groups
• On the Gross-Prasad conjecture with its refinement for $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$ and the generalized Böcherer conjecture