JournalsdmOnline First

Constructing vector-valued automorphic forms on unitary groups

  • Thomas Browning

    University of California, Berkeley, USA

  • Pavel Čoupek

    Michigan State University, East Lansing, USA; University of Virginia, Charlottesville, USA

  • Ellen Eischen

    University of Oregon, Eugene, USA

  • Claire Frechette

    Boston College, Chestnut Hill, USA; Umeå University, Sweden

  • Serin Hong

    University of Arizona, Tucson, USA

  • Si Ying Lee

    Stanford University, USA; National University of Singapore, Singapore

  • David Marcil

    Columbia University, New York, USA; University of Oregon, Eugene, USA
Constructing vector-valued automorphic forms on unitary groups cover
Download PDF

This article is published open access.

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 Cléry 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 this article

Thomas Browning, Pavel Čoupek, Ellen Eischen, Claire Frechette, Serin Hong, Si Ying Lee, David Marcil, Constructing vector-valued automorphic forms on unitary groups. Doc. Math. (2026), published online first

DOI 10.4171/DM/1065