Rankin--Cohen Type Differential Operators on Hermitian Modular Forms

Francis Dunn

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arXiv · 2404.04371

Rankin--Cohen Type Differential Operators on Hermitian Modular Forms

Francis Dunn

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Abstract

We construct Rankin-Cohen type differential operators on Hermitian modular forms of signature $(n,n)$. The bilinear differential operators given here specialize to the original Rankin-Cohen operators in the case $n=1$, and more generally satisfy some analogous properties, including uniqueness. Our approach builds on previous work by Eholzer-Ibukiyama in the case of Siegel modular forms, together with results of Kashiwara-Vergne on the representation theory of unitary groups.

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Francis Dunn. 2024-04-05. Rankin--Cohen Type Differential Operators on Hermitian Modular Forms. https://arxiv.org/abs/2404.04371

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