Constructing vector-valued automorphic forms on unitary groups
Number Theory
2026-05-28 v2
Abstract
We introduce a method for producing vector-valued automorphic forms on unitary groups from scalar-valued ones. As an application, we construct an explicit example. Our strategy employs certain differential operators. It is inspired by work of Cl\'ery and van der Geer in the setting of Siegel modular forms, but it also requires overcoming challenges that do not arise in the Siegel setting.
Cite
@article{arxiv.2408.05198,
title = {Constructing vector-valued automorphic forms on unitary groups},
author = {Thomas L. Browning and Pavel Čoupek and Ellen Eischen and Claire Frechette and Serin Hong and Si Ying Lee and David Marcil},
journal= {arXiv preprint arXiv:2408.05198},
year = {2026}
}
Comments
35 pages. Rewrote Section 5