Arthur's multiplicity formula for even orthogonal and unitary groups

TL;DR

This paper proves Arthur's multiplicity formula for the automorphic discrete spectrum of even orthogonal and unitary groups over number fields, using theta lifts, and extends results to certain non-generic cases.

Contribution

It establishes Arthur's multiplicity formula for generic and some non-generic A-parameters for these groups, providing a full description of their automorphic spectra.

Findings

Proves multiplicity formula for generic automorphic representations.

Extends multiplicity results to non-generic A-parameters.

Describes the automorphic spectrum for groups with Witt index ≤ 1.

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.