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arXiv · 2408.05198

Constructing vector-valued automorphic forms on unitary groups

Thomas L. Browning·Pavel Čoupek·Ellen Eischen·Claire Frechette·Serin Hong·Si Ying Lee·David Marcil
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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.

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Thomas L. Browning, Pavel Čoupek, Ellen Eischen, Claire Frechette, Serin Hong, Si Ying Lee, David Marcil. 2024-08-09. Constructing vector-valued automorphic forms on unitary groups. https://doi.org/10.4171/dm/1065

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