Theta Correspondence and Arthur packets

TL;DR

This paper proves the independence of local packets in Arthur's multiplicity formula for certain groups at non-Archimedean places and confirms their equivalence to Arthur/Mok's local A-packets in quasi-split cases.

Contribution

It establishes the independence of local packets from dual-pair choices and their equivalence to known A-packets for specific groups.

Findings

Local packets are independent of dual-pair choices at non-Archimedean places.

In quasi-split cases, local packets match Arthur/Mok's A-packets.

The results extend the understanding of Arthur's multiplicity formula for orthogonal and unitary groups.

Abstract

In spirit of Gan-Ichino's work on the Arthur's multiplicity formula for metaplectic groups, we have established the Arthur's multiplicity formula for even orthogonal or unitary groups with Witt index less than or equal to one. In that multiplicity formula, some local packets defined using the stable range theta lifts are involved. In this paper, we prove that at non-Archimedean places, the definition of the local packets involved in that multiplicity formula is independent of the choice of the dual-pairs used in their construction. Moreover, at those places where the groups are quasi-split, we prove that the local packets involved are the same as the local A-packets defined by Arthur/ Mok.