Limit Multiplicity For Unitary Groups and The Stable Trace Formula

TL;DR

This paper establishes upper bounds on the limit multiplicities of certain non-tempered representations of unitary groups, with applications to the growth of cohomology in arithmetic subgroups, using advanced trace formula techniques.

Contribution

It provides new bounds on limit multiplicities for non-tempered representations of unitary groups, leveraging Arthur's trace formula and endoscopic classification.

Findings

Upper bounds on limit multiplicities for specific representations

Applications to cohomology growth in arithmetic subgroups

Utilization of endoscopic transfer and trace formula stabilization

Abstract

We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic subgroups of unitary groups. The representations considered are transfers of products of characters and discrete series on endoscopic groups, and the bounds are obtained using Arthur's stabilization of the trace formula and the endoscopic classification of representations due to Mok and Kaletha-Minguez-Shin-White.