Rankin--Cohen Type Differential Operators on Hermitian Modular Forms

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.