Arthur's multiplicity formula for even orthogonal and unitary groups

Abstract

Let G be an even orthogonal or unitary group over a number field. Based on the same observation used in arXiv:1705.10106, we prove the Arthur's multiplicity formula for the generic part of the automorphic discrete spectrum of G by using the theta lift. We also consider a class of non-generic A-parameters and obtain a multiplicity formula in this case. In particular, we obtain a description of the full automorphic discrete spectrum of even orthogonal or unitary groups with Witt index less or equal to one.

61 pages, accepted for publication in JEMS, minor revisions included