Endoscopic Transfer of Automorphic Representations for Unitary Groups over Function Fields

This monograph establishes a rigorous framework for the endoscopic transfer of automorphic representations from quasi-split unitary groups U(n) to general linear groups GL(n) over a global function field F of characteristic p > 0. We invoke the Arthur-Selberg trace formula in its stable form, leveraging the proof of the Fundamental Lemma by Ngô B Châu to stabilize the geometric side of the trace formula. By constructing a correspondence between the stable tempered characters of U(n) and the twisted characters of GL(n), we characterize the discrete automorphic spectrum of U(n) in terms of isobaric automorphic representations of general linear groups. The analysis encompasses the definition of local and global transfer factors, the stabilization of elliptic orbital integrals, and the spectral decomposition of the L2-space of automorphic forms. We further discuss the structure of local L-packets and the multiplicity formula for the discrete spectrum, providing a function-field analogue to the endoscopic classification known for number fields.