Limit multiplicity for unitary groups and the stable trace formula

Gerbelli-Gauthier, Mathilde

doi:10.2140/ant.2023.17.2181

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Limit multiplicity for unitary groups and the stable trace formula

Mathilde Gerbelli-Gauthier

Vol. 17 (2023), No. 12, 2181–2228

DOI: 10.2140/ant.2023.17.2181

Abstract

We give upper bounds on limit multiplicities of certain nontempered representations of unitary groups $U (a, b)$ , conditionally on the endoscopic classification of representations. Our result applies to 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 classification established by Mok, and Kaletha, Minguez, Shin and White.

Keywords

automorphic representations, unitary groups, limit multiplicity

Mathematical Subject Classification

Primary: 11F55, 11F72, 11F75

Milestones

Received: 11 April 2022

Revised: 21 September 2022

Accepted: 6 March 2023

Published: 8 October 2023

Authors

Mathilde Gerbelli-Gauthier
Department of Mathematics and Statistics McGill University Montreal Canada

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Vol. 17, No. 12, 2023