  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.
