Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions

Abstract

The global twisted GGP conjecture is a variant of the Gan-Gross-Prasad conjecture for unitary groups, and considers the restriction of an automorphic representation of GL(V ) to its subgroup U(V ), for a skew-Hermitian space V. It relates the nonvanishing of a certain period integral to the central value of an L-function attached to the representation.

In this thesis, using a relative trace formula approach, we prove the global twisted GGP conjecture in the unramified case, under some additional local assumptions on the quadratic extension and the automorphic representation. In particular, we reduce the required fundamental lemma to the Jacquet-Rallis fundamental lemma.